Yampa

NOTES FROM SF:

FOR STEAMBOAT, COMPARE THE DETRENDED CLIAMTE NORMAL CURVES AGAINST EACH OTHER

Derry & fassnacht 2010 Compare climatology of SNOTEL stations= they don’t have the same climatol9ogy based on the snow data

Figure 5b - https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2009WR007835

Disclaimer

This work is very preliminary as I get back into the coding swing of things. Data wrangling and figure generation will be done via R, but the rest of the project will be done using good ol’ microsoft products. This is just an entry point into data crunching and should by no means be considered a final product.

Also, I’m not great at this but whatever. I could automate this, but I’ll figure that out shortly!

Need to update figures & analyze sites for seasonal trends

Methodology

SNOTEL data was provided by the NRCS. Data was cleaned by removing outliers that are likely implausible; any year with more than 15 observations missing was removed. Temperatures were adjusted using the Morrisey method for stations identified by Ma et al (2019) due to SNOTEL temperature sensor changes, with the adjustment applied to pre-sensor change data. Daily mean observations were detrended to determine whether values were increasing or decreasing from the entire time series trend. Daily mean temperatures were first averaged by water year, with all water year means then averaged by day of water year. The mean temperature by day for the period of record was averaged. To find the standard deviation, the daily mean temperatures by water year was subtracted from the averaged mean temperature by day for the period of record. All water year means averaged by day of water year were subtracted from the temperature mean. The resulting values were then added together to find the “residual” of the daily mean temperatures by water year. The standard deviation was then computed from those residuals, with trends analyzed by Mann‐Kendall significance test and Theil‐Sen’s rate of change. Significant trends are identified with p-values of less than 0.10.

Morrisey Method

The Morrisey Method is taken from Ma, Fassnacht and Kampf..

In R script: T(adjusted) = 5.3x10^(-7)xT(old)4+3.72x10^(-5)xT(old)3-2.16x10^(-3)xT(old)2-7.32x10^(-2)xT(old)+1.37

In the Ma et al. spreadsheet, H1 is Morrisey, H2 is Oiler

3/01 update

Analyzing by summer and winter seasons for each station’s timeseries, using the shifted mean of the time series, then sigmoidal detrending. Standard deviation is taken with the relevant days of the water year.

3/06 update

Analyzing for spring and fall….

Yampa Area SNOTEL sites:

Burro Mountain 378 NSCE- Original, Bias- Morrisey 7/11/2002 (NSCE- 0.87 vs 0.84, Bias- -0.03 vs. 0.11)

Columbine 408 Morrisey 7/22/2005

Columbine Pass 409 Morrisey 6/23/2005

Crosho 426 Morrisey 7/21/2005

Dry Lake 457 Oyler -> Morrisey 7/30/2003

Elk River 467 Oyler -> Morrisey 8/7/2006

Lynx Pass 607 Morrisey 5/22/2006

Rabbit Ears 709 Morrisey 8/7/2006 (Does not go.)

Ripple Creek 717 Oyler -> Morrisey 8/7/2006

Tower 825 Original 8/18/2004

Trapper Lake 827 Original 12/13/2004

Data from thesis research:

SNOTEL_yampa_area <- snotel_download(site_id = c(378, 408, 409, 426, 457, 467, 607, 709, 717, 825, 827), path = tempdir('../data'), internal = TRUE)

write.csv(SNOTEL_yampa_area,"C:/Users/13074/Documents/ESS580/thesis_project/Yampa/data_raw/snotel_yampa.csv", row.names = FALSE) #write in the raw data

SNOTEL_yampa_area <- read.csv("C:/Users/13074/Documents/ESS580/thesis_project/Yampa/data_raw/snotel_yampa.csv", header = TRUE)

Burro Mountain 378

NSCE- Original, Bias- Morrisey 7/11/2002 so, ORIGINAL. Morrisey is marked as having the smallest bias, but the sheet says original is smaller.

snotel_378 <- SNOTEL_yampa_area %>% 
  filter(site_id == "378")

#str(snotel_378) # check the date, usually a character.  

snotel_378$Date <- as.Date(snotel_378$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_378_clean <- snotel_378 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_378_clean <- snotel_378_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_378_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_378_clean <- snotel_378_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -40)# %>% 
  #filter(temperature_mean < 25)

ggplot(snotel_378_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_378_cull_count <- snotel_378_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_378_cull_count

# filtering for too few observations in a year
snotel_378_cull_count_days <- snotel_378_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_378_cull_count_days

## # A tibble: 10 x 2
## # Groups:   waterYear [10]
##    waterYear     n
##        <dbl> <int>
##  1      1985     1
##  2      1988   298
##  3      1989   341
##  4      1993   281
##  5      1994   261
##  6      1995   344
##  7      1996   320
##  8      2002   312
##  9      2016   310
## 10      2022   338

snotel_378_clean_culled <- snotel_378_clean %>% 
  filter(waterYear != "1985" & waterYear != "1986" & waterYear != "1988" & waterYear != "1989" & waterYear != "1993" & waterYear != "1994" & waterYear != "1995" & waterYear != "1996" & waterYear != "2002" & waterYear != "2016" & waterYear != "2022")# & waterYear != "2017") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_378_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Culling WY 1986 as well.

ggplot(snotel_378_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_378_xts <- xts(snotel_378_clean_culled$temperature_mean, order.by = snotel_378_clean_culled$Date)

dygraph(temp_378_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

#snotel_378_clean_culled <- snotel_378_clean_culled %>% 
#  filter(temperature_mean < 19.3)

temp_378_xts <- xts(snotel_378_clean_culled$temperature_mean, order.by = snotel_378_clean_culled$Date)

dygraph(temp_378_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

Burro Mountain 378

NSCE- Original, Bias- Morrisey 7/11/2002

snotel_378_adjusted <- snotel_378_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2002-07-11", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

378 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_378 <- snotel_378_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_378 <- yearly_wy_aver_378 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_378 <- daily_wy_aver_378 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_378$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_378 <-daily_wy_aver_378 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_378$date_temp <- signif(daily_wy_aver2_378$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_378, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

378 SD

standard_dev_378 <- daily_wy_aver_378 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

standard_dev_all_378 <- standard_dev_378 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_378 <- standard_dev_all_378 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_378 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.844333
1990	3.840459
1991	4.152285
1992	3.762154
1997	3.990912
1998	3.720044
1999	3.917633
2000	3.912993
2001	3.855899
2003	3.665924
2004	4.000526
2005	3.480996
2006	3.976868
2007	3.874997
2008	3.754838
2009	3.615420
2010	3.592359
2011	3.866506
2012	3.431475
2013	4.071795
2014	3.589962
2015	3.810310
2017	4.047282
2018	3.371707
2019	3.627857
2020	4.080397
2021	3.694656

ggplot(standard_dev_all_378, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 378 average temperatures for water years 2005-2021

MK & SS for 378 (non-corrected)

sd_mk_378 <- mk.test(standard_dev_all_378$sd_2)
print(sd_mk_378)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_378$sd_2
## z = -1.2925, n = 27, p-value = 0.1962
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -63.0000000 2301.0000000   -0.1794872

sd_sens_378 <- sens.slope(standard_dev_all_378$sd_2)
print(sd_sens_378)

## 
##  Sen's slope
## 
## data:  standard_dev_all_378$sd_2
## z = -1.2925, n = 27, p-value = 0.1962
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.019352100  0.004261212
## sample estimates:
## Sen's slope 
## -0.00808587

Corrected

378 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_378_ad <- snotel_378_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_378_ad <- yearly_wy_aver_378_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_378_ad <- daily_wy_aver_378_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_378_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_378_ad <-daily_wy_aver_378_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_378_ad$date_temp_ad <- signif(daily_wy_aver2_378_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_378_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

378 SS (corrected)

standard_dev_378_ad <- daily_wy_aver_378_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_378_ad <- standard_dev_378_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_378_ad <- standard_dev_all_378_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_378_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.635402
1990	3.571781
1991	3.924198
1992	3.584506
1997	3.765809
1998	3.444660
1999	3.756325
2000	3.657796
2001	3.547148
2003	3.673553
2004	3.964851
2005	3.451173
2006	3.977442
2007	3.892954
2008	3.772474
2009	3.580080
2010	3.606648
2011	3.854514
2012	3.440420
2013	4.091489
2014	3.578326
2015	3.765488
2017	4.016757
2018	3.358551
2019	3.638647
2020	4.095520
2021	3.711136

ggplot(standard_dev_all_378_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 378 average temperatures for water years 1986-2021

MK & SS 378 (corrected)

sd_mk_378_ad <- mk.test(standard_dev_all_378_ad$sd_2)
print(sd_mk_378_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_378_ad$sd_2
## z = 0.79218, n = 27, p-value = 0.4283
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   39.0000000 2301.0000000    0.1111111

sd_sens_378_ad <- sens.slope(standard_dev_all_378_ad$sd_2)
print(sd_sens_378_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_378_ad$sd_2
## z = 0.79218, n = 27, p-value = 0.4283
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.008353158  0.016292391
## sample estimates:
## Sen's slope 
## 0.004238996

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_378 <- standard_dev_378 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_378 <- summer_standard_dev_all_378 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_378 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.519944
1990	2.991647
1991	2.301635
1992	2.927244
1997	2.299028
1998	3.216968
1999	2.179241
2000	2.566396
2001	2.907393
2003	2.553179
2004	2.698694
2005	2.848247
2006	2.501620
2007	2.191416
2008	2.404034
2009	2.037832
2010	2.234948
2011	2.097951
2012	2.150713
2013	2.143274
2014	2.308825
2015	2.440864
2017	2.056110
2018	2.073730
2019	2.585254
2020	2.839585
2021	2.914442

ggplot(summer_standard_dev_all_378, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 378 average summer temperatures for water years 2005-2021

summer MK & SS for 378 (non-corrected)

summer_sd_mk_378 <- mk.test(summer_standard_dev_all_378$sd_2)
print(summer_sd_mk_378)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_378$sd_2
## z = -1.7094, n = 27, p-value = 0.08737
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -83.0000000 2301.0000000   -0.2364672

summer_sd_sens_378 <- sens.slope(summer_standard_dev_all_378$sd_2)
print(summer_sd_sens_378)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_378$sd_2
## z = -1.7094, n = 27, p-value = 0.08737
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.034019036  0.002611249
## sample estimates:
## Sen's slope 
##  -0.0129552

Winter

winter_standard_dev_all_378 <- standard_dev_378 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_378 <- winter_standard_dev_all_378 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_378 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.646858
1990	4.370827
1991	4.893370
1992	3.795916
1997	4.633640
1998	4.083586
1999	4.571204
2000	4.339714
2001	4.224920
2003	4.301637
2004	4.571834
2005	4.035326
2006	4.785264
2007	4.776866
2008	4.520852
2009	4.333085
2010	3.993484
2011	4.884186
2012	4.032196
2013	5.013664
2014	3.967656
2015	4.595698
2017	4.647297
2018	3.969930
2019	4.148917
2020	4.007006
2021	4.017442

ggplot(winter_standard_dev_all_378, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 378 average winter temperatures for water years 2005-2021

winter MK & SS for 378 (non-corrected)

winter_sd_mk_378 <- mk.test(winter_standard_dev_all_378$sd_2)
print(winter_sd_mk_378)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_378$sd_2
## z = -1.2508, n = 27, p-value = 0.211
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -61.0000000 2301.0000000   -0.1737892

winter_sd_sens_378 <- sens.slope(winter_standard_dev_all_378$sd_2)
print(winter_sd_sens_378)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_378$sd_2
## z = -1.2508, n = 27, p-value = 0.211
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.028694833  0.009594993
## sample estimates:
##  Sen's slope 
## -0.009648291

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_378_ad <- standard_dev_378_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_378_ad <- summer_standard_dev_all_378_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_378_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.281137
1990	2.706950
1991	2.081504
1992	2.638399
1997	2.077041
1998	2.852230
1999	1.949459
2000	2.312759
2001	2.628411
2003	2.571301
2004	2.681783
2005	2.871469
2006	2.488610
2007	2.201130
2008	2.421151
2009	2.047690
2010	2.234717
2011	2.097755
2012	2.138574
2013	2.126970
2014	2.305642
2015	2.428691
2017	2.041059
2018	2.059623
2019	2.594543
2020	2.825679
2021	2.881607

ggplot(summer_standard_dev_all_378_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 378 average summer temperatures for water years 1986-2021

summer MK & SS 378 (corrected)

summer_sd_mk_378_ad <- mk.test(summer_standard_dev_all_378_ad$sd_2)
print(summer_sd_mk_378_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_378_ad$sd_2
## z = -0.25016, n = 27, p-value = 0.8025
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -13.00000000 2301.00000000   -0.03703704

summer_sd_sens_378_ad <- sens.slope(summer_standard_dev_all_378_ad$sd_2)
print(summer_sd_sens_378_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_378_ad$sd_2
## z = -0.25016, n = 27, p-value = 0.8025
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02112144  0.01493032
## sample estimates:
## Sen's slope 
## -0.00199902

Winter

winter_standard_dev_all_378_ad <- standard_dev_378_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_378_ad <- winter_standard_dev_all_378_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_378_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.486747
1990	4.205583
1991	4.783651
1992	3.673412
1997	4.452262
1998	3.932303
1999	4.376905
2000	4.129924
2001	4.097792
2003	4.290050
2004	4.572725
2005	4.023538
2006	4.782438
2007	4.783581
2008	4.527273
2009	4.330641
2010	3.996081
2011	4.876192
2012	4.033049
2013	5.012588
2014	3.965097
2015	4.592748
2017	4.659374
2018	3.968231
2019	4.140915
2020	4.005496
2021	4.012923

ggplot(winter_standard_dev_all_378_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 378 average winter temperatures for water years 1986-2021

winter MK & SS 378 (corrected)

winter_sd_mk_378_ad <- mk.test(winter_standard_dev_all_378_ad$sd_2)
print(winter_sd_mk_378_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_378_ad$sd_2
## z = -0.29186, n = 27, p-value = 0.7704
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -15.00000000 2301.00000000   -0.04273504

winter_sd_sens_378_ad <- sens.slope(winter_standard_dev_all_378_ad$sd_2)
print(winter_sd_sens_378_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_378_ad$sd_2
## z = -0.29186, n = 27, p-value = 0.7704
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02107667  0.01715794
## sample estimates:
##  Sen's slope 
## -0.003978539

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_378 <- standard_dev_378 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_378 <- spring_standard_dev_all_378 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_378 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.692000
1990	3.410893
1991	4.412912
1992	3.202418
1997	4.253521
1998	3.237115
1999	4.006045
2000	4.504179
2001	3.709817
2003	3.947462
2004	3.492848
2005	3.400284
2006	3.208628
2007	3.738166
2008	3.490849
2009	3.341240
2010	3.938693
2011	3.492053
2012	3.527092
2013	4.172600
2014	4.129458
2015	3.192933
2017	4.283350
2018	3.176609
2019	3.637517
2020	3.741933
2021	3.465805

ggplot(spring_standard_dev_all_378, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 378 average spring temperatures for water years 2005-2021

spring MK & SS for 378 (non-corrected)

spring_sd_mk_378 <- mk.test(spring_standard_dev_all_378$sd_2)
print(spring_sd_mk_378)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_378$sd_2
## z = -0.50033, n = 27, p-value = 0.6168
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -25.00000000 2301.00000000   -0.07122507

spring_sd_sens_378 <- sens.slope(spring_standard_dev_all_378$sd_2)
print(spring_sd_sens_378)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_378$sd_2
## z = -0.50033, n = 27, p-value = 0.6168
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02833277  0.01824868
## sample estimates:
##  Sen's slope 
## -0.002916373

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_378 <- standard_dev_378 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_378 <- fall_standard_dev_all_378 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_378 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.375846
1990	3.739173
1991	3.796365
1992	4.431350
1997	4.026441
1998	3.731377
1999	3.512352
2000	3.758627
2001	3.237668
2003	2.778814
2004	4.158417
2005	2.524635
2006	3.922491
2007	3.365913
2008	3.451126
2009	3.299940
2010	3.875278
2011	2.997593
2012	3.008296
2013	3.349090
2014	3.597650
2015	3.111683
2017	4.013998
2018	3.456008
2019	3.550635
2020	5.506487
2021	4.064501

ggplot(fall_standard_dev_all_378, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 378 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 378 (non-corrected)

fall_sd_mk_378 <- mk.test(fall_standard_dev_all_378$sd_2)
print(fall_sd_mk_378)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_378$sd_2
## z = -0.083388, n = 27, p-value = 0.9335
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##   -5.00000000 2301.00000000   -0.01424501

fall_sd_sens_378 <- sens.slope(fall_standard_dev_all_378$sd_2)
print(fall_sd_sens_378)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_378$sd_2
## z = -0.083388, n = 27, p-value = 0.9335
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.03098797  0.02672952
## sample estimates:
##  Sen's slope 
## -0.001408189

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_378_ad <- standard_dev_378_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_378_ad <- spring_standard_dev_all_378_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_378_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.415274
1990	3.163959
1991	4.066110
1992	2.979428
1997	3.936885
1998	2.925370
1999	3.692620
2000	4.111739
2001	3.408605
2003	3.955374
2004	3.481716
2005	3.399557
2006	3.193743
2007	3.731619
2008	3.503981
2009	3.355240
2010	3.941205
2011	3.478097
2012	3.508195
2013	4.184425
2014	4.134220
2015	3.151142
2017	4.261683
2018	3.195918
2019	3.597782
2020	3.760857
2021	3.464185

ggplot(spring_standard_dev_all_378_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 378 average spring temperatures for water years 1986-2021

spring MK & SS 378 (corrected)

spring_sd_mk_378_ad <- mk.test(spring_standard_dev_all_378_ad$sd_2)
print(spring_sd_mk_378_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_378_ad$sd_2
## z = 0.91726, n = 27, p-value = 0.359
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   45.0000000 2301.0000000    0.1282051

spring_sd_sens_378_ad <- sens.slope(spring_standard_dev_all_378_ad$sd_2)
print(spring_sd_sens_378_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_378_ad$sd_2
## z = 0.91726, n = 27, p-value = 0.359
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01536871  0.02944544
## sample estimates:
## Sen's slope 
## 0.007604482

Fall

fall_standard_dev_all_378_ad <- standard_dev_378_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_378_ad <- fall_standard_dev_all_378_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_378_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.146701
1990	3.368817
1991	3.532874
1992	4.129006
1997	3.689817
1998	3.343434
1999	3.308209
2000	3.472583
2001	2.929131
2003	2.772175
2004	4.098027
2005	2.531244
2006	3.879968
2007	3.400007
2008	3.415639
2009	3.289946
2010	3.900149
2011	2.973635
2012	3.017688
2013	3.356596
2014	3.612165
2015	3.072767
2017	3.975535
2018	3.463087
2019	3.568716
2020	5.544390
2021	4.071006

ggplot(fall_standard_dev_all_378_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 378 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 378 (corrected)

fall_sd_mk_378_ad <- mk.test(fall_standard_dev_all_378_ad$sd_2)
print(fall_sd_mk_378_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_378_ad$sd_2
## z = 1.084, n = 27, p-value = 0.2783
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   53.0000000 2301.0000000    0.1509972

fall_sd_sens_378_ad <- sens.slope(fall_standard_dev_all_378_ad$sd_2)
print(fall_sd_sens_378_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_378_ad$sd_2
## z = 1.084, n = 27, p-value = 0.2783
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01036929  0.03886043
## sample estimates:
## Sen's slope 
##  0.01311408

Columbine 408

Morrisey 7/22/2005

snotel_408 <- SNOTEL_yampa_area %>% 
  filter(site_id == "408")

#str(snotel_408) # check the date, usually a character.  

snotel_408$Date <- as.Date(snotel_408$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_408_clean <- snotel_408 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_408_clean <- snotel_408_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_408_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_408_clean <- snotel_408_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -40)# %>% 
  #filter(temperature_mean < 25)

ggplot(snotel_408_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_408_cull_count <- snotel_408_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_408_cull_count

# filtering for too few observations in a year
snotel_408_cull_count_days <- snotel_408_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_408_cull_count_days

## # A tibble: 8 x 2
## # Groups:   waterYear [8]
##   waterYear     n
##       <dbl> <int>
## 1      1981   343
## 2      1983   317
## 3      1984   234
## 4      1985   195
## 5      1986   336
## 6      1987   298
## 7      1994   272
## 8      2002   347

snotel_408_clean_culled <- snotel_408_clean %>% 
  filter(waterYear > "1987" & waterYear != "1993" & waterYear != "1994" & waterYear != "2002")# & waterYear != "1985" & waterYear != "1986" & waterYear != "1987" & waterYear != "1994" & waterYear != "2002")# & waterYear != "2002" & waterYear != "2016" & waterYear != "2022")# & waterYear != "2017") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_408_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Culling WY 1986 & 1993 as well.

ggplot(snotel_408_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_408_xts <- xts(snotel_408_clean_culled$temperature_mean, order.by = snotel_408_clean_culled$Date)

dygraph(temp_408_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

snotel_408_clean_culled <- snotel_408_clean_culled %>% 
  filter(temperature_mean > -30)

temp_408_xts <- xts(snotel_408_clean_culled$temperature_mean, order.by = snotel_408_clean_culled$Date)

dygraph(temp_408_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

Columbine 408 Morrisey 7/22/2005

snotel_408_adjusted <- snotel_408_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2005-07-22", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

408 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_408 <- snotel_408_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_408 <- yearly_wy_aver_408 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_408 <- daily_wy_aver_408 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_408$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_408 <-daily_wy_aver_408 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_408$date_temp <- signif(daily_wy_aver2_408$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_408, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

408 SD

standard_dev_408 <- daily_wy_aver_408 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

#detrend check:

detrend_check <- standard_dev_408 %>% 
  filter(waterYear == 2000)

#Testing:

ggplot(detrend_check, aes(x = waterDay, y = residual))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

standard_dev_all_408 <- standard_dev_408 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_408 <- standard_dev_all_408 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_408 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	4.122196
1989	4.224835
1990	3.532619
1991	3.912811
1992	3.818307
1995	3.854523
1996	3.890789
1997	3.911970
1998	3.624131
1999	3.893187
2000	3.713913
2001	3.755341
2003	3.603353
2004	3.901334
2005	3.505008
2006	3.862466
2007	3.764506
2008	3.618292
2009	3.658604
2010	3.618734
2011	3.667218
2012	3.498434
2013	3.927084
2014	3.637173
2015	3.865239
2016	3.367491
2017	4.108813
2018	3.452191
2019	3.546643
2020	3.934865
2021	3.594691
2022	3.887378

ggplot(standard_dev_all_408, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 408 average temperatures for water years 2005-2021

MK & SS for 408 (non-corrected)

sd_mk_408 <- mk.test(standard_dev_all_408$sd_2)
print(sd_mk_408)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_408$sd_2
## z = -1.8, n = 32, p-value = 0.07186
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -112.0000000 3802.6666667   -0.2258065

sd_sens_408 <- sens.slope(standard_dev_all_408$sd_2)
print(sd_sens_408)

## 
##  Sen's slope
## 
## data:  standard_dev_all_408$sd_2
## z = -1.8, n = 32, p-value = 0.07186
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.0178517126  0.0007511908
## sample estimates:
##  Sen's slope 
## -0.009022314

Corrected

408 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_408_ad <- snotel_408_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_408_ad <- yearly_wy_aver_408_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_408_ad <- daily_wy_aver_408_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_408_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_408_ad <-daily_wy_aver_408_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_408_ad$date_temp_ad <- signif(daily_wy_aver2_408_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_408_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

408 SS (corrected)

standard_dev_408_ad <- daily_wy_aver_408_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_408_ad <- standard_dev_408_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_408_ad <- standard_dev_all_408_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_408_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	3.850953
1989	3.996876
1990	3.330601
1991	3.726679
1992	3.669064
1995	3.666226
1996	3.689966
1997	3.722851
1998	3.379176
1999	3.744324
2000	3.502298
2001	3.481885
2003	3.367334
2004	3.706363
2005	3.377878
2006	3.865469
2007	3.784549
2008	3.644975
2009	3.609154
2010	3.636002
2011	3.660927
2012	3.513289
2013	3.958862
2014	3.617062
2015	3.800511
2016	3.366825
2017	4.065810
2018	3.424283
2019	3.561106
2020	3.962227
2021	3.622561
2022	3.888948

ggplot(standard_dev_all_408_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 408 average temperatures for water years 1986-2021

MK & SS 408 (corrected)

sd_mk_408_ad <- mk.test(standard_dev_all_408_ad$sd_2)
print(sd_mk_408_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_408_ad$sd_2
## z = 0.081082, n = 32, p-value = 0.9354
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 6.000000e+00 3.802667e+03 1.209677e-02

sd_sens_408_ad <- sens.slope(standard_dev_all_408_ad$sd_2)
print(sd_sens_408_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_408_ad$sd_2
## z = 0.081082, n = 32, p-value = 0.9354
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.007237353  0.010756670
## sample estimates:
##  Sen's slope 
## 0.0009834684

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_408 <- standard_dev_408 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_408 <- summer_standard_dev_all_408 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_408 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	2.160058
1989	3.008387
1990	2.733971
1991	2.409098
1992	2.549817
1995	3.208616
1996	1.630178
1997	2.159624
1998	3.030893
1999	1.872728
2000	2.406849
2001	2.827944
2003	2.775887
2004	2.802336
2005	2.735618
2006	2.408819
2007	2.215970
2008	2.558499
2009	2.142990
2010	2.171074
2011	1.985865
2012	2.183402
2013	2.179981
2014	2.111047
2015	2.225452
2016	2.085728
2017	1.970802
2018	2.192960
2019	2.410520
2020	2.454214
2021	2.777513
2022	2.159458

ggplot(summer_standard_dev_all_408, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 408 average summer temperatures for water years 2005-2021

summer MK & SS for 408 (non-corrected)

summer_sd_mk_408 <- mk.test(summer_standard_dev_all_408$sd_2)
print(summer_sd_mk_408)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_408$sd_2
## z = -1.6379, n = 32, p-value = 0.1015
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -102.0000000 3802.6666667   -0.2056452

summer_sd_sens_408 <- sens.slope(summer_standard_dev_all_408$sd_2)
print(summer_sd_sens_408)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_408$sd_2
## z = -1.6379, n = 32, p-value = 0.1015
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.0285029383  0.0009541897
## sample estimates:
## Sen's slope 
## -0.01383851

Winter

winter_standard_dev_all_408 <- standard_dev_408 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_408 <- winter_standard_dev_all_408 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_408 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	4.680675
1989	4.973300
1990	4.039090
1991	4.634553
1992	3.838325
1995	4.621117
1996	4.536271
1997	4.561342
1998	4.041858
1999	4.581090
2000	4.077551
2001	4.030738
2003	3.960560
2004	4.319515
2005	4.197485
2006	4.636681
2007	4.627002
2008	4.199476
2009	4.398940
2010	4.095228
2011	4.617140
2012	4.121452
2013	4.792809
2014	4.110372
2015	4.813936
2016	4.119557
2017	4.891639
2018	4.056260
2019	4.052562
2020	3.806438
2021	3.872154
2022	4.699146

ggplot(winter_standard_dev_all_408, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 408 average winter temperatures for water years 2005-2021

winter MK & SS for 408 (non-corrected)

winter_sd_mk_408 <- mk.test(winter_standard_dev_all_408$sd_2)
print(winter_sd_mk_408)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_408$sd_2
## z = -0.76217, n = 32, p-value = 0.446
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -48.00000000 3802.66666667   -0.09677419

winter_sd_sens_408 <- sens.slope(winter_standard_dev_all_408$sd_2)
print(winter_sd_sens_408)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_408$sd_2
## z = -0.76217, n = 32, p-value = 0.446
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.024067288  0.005552547
## sample estimates:
##  Sen's slope 
## -0.007399084

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_408_ad <- standard_dev_408_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_408_ad <- summer_standard_dev_all_408_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_408_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	1.951149
1989	2.691408
1990	2.468482
1991	2.173205
1992	2.296903
1995	2.882685
1996	1.459462
1997	1.948304
1998	2.703351
1999	1.674073
2000	2.171356
2001	2.547978
2003	2.453149
2004	2.523349
2005	2.479412
2006	2.387287
2007	2.233782
2008	2.581903
2009	2.162547
2010	2.166643
2011	1.988990
2012	2.156846
2013	2.151757
2014	2.103464
2015	2.191604
2016	2.052962
2017	1.940250
2018	2.174709
2019	2.430984
2020	2.442469
2021	2.744131
2022	2.151181

ggplot(summer_standard_dev_all_408_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 408 average summer temperatures for water years 1986-2021

summer MK & SS 408 (corrected)

summer_sd_mk_408_ad <- mk.test(summer_standard_dev_all_408_ad$sd_2)
print(summer_sd_mk_408_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_408_ad$sd_2
## z = -0.8919, n = 32, p-value = 0.3724
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -56.0000000 3802.6666667   -0.1129032

summer_sd_sens_408_ad <- sens.slope(summer_standard_dev_all_408_ad$sd_2)
print(summer_sd_sens_408_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_408_ad$sd_2
## z = -0.8919, n = 32, p-value = 0.3724
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.017755194  0.008453193
## sample estimates:
##  Sen's slope 
## -0.004192841

Winter

winter_standard_dev_all_408_ad <- standard_dev_408_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_408_ad <- winter_standard_dev_all_408_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_408_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	4.570065
1989	4.851524
1990	3.911990
1991	4.548088
1992	3.740151
1995	4.454623
1996	4.397209
1997	4.411526
1998	3.909249
1999	4.427019
2000	3.900180
2001	3.925081
2003	3.830604
2004	4.157215
2005	4.075941
2006	4.636058
2007	4.635832
2008	4.205165
2009	4.395215
2010	4.098594
2011	4.612482
2012	4.123831
2013	4.790447
2014	4.108958
2015	4.809684
2016	4.115105
2017	4.906039
2018	4.048838
2019	4.039119
2020	3.806029
2021	3.863195
2022	4.696385

ggplot(winter_standard_dev_all_408_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 408 average winter temperatures for water years 1986-2021

winter MK & SS 408 (corrected)

winter_sd_mk_408_ad <- mk.test(winter_standard_dev_all_408_ad$sd_2)
print(winter_sd_mk_408_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_408_ad$sd_2
## z = -0.24325, n = 32, p-value = 0.8078
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -16.00000000 3802.66666667   -0.03225806

winter_sd_sens_408_ad <- sens.slope(winter_standard_dev_all_408_ad$sd_2)
print(winter_sd_sens_408_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_408_ad$sd_2
## z = -0.24325, n = 32, p-value = 0.8078
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01822521  0.01275575
## sample estimates:
##  Sen's slope 
## -0.001834189

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_408 <- standard_dev_408 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_408 <- spring_standard_dev_all_408 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_408 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	4.025326
1989	4.187649
1990	3.169213
1991	3.931048
1992	3.316353
1995	2.858090
1996	3.930483
1997	4.079687
1998	3.011379
1999	4.204134
2000	4.312522
2001	3.756611
2003	4.197188
2004	3.802792
2005	3.259969
2006	3.209573
2007	3.581505
2008	3.572901
2009	3.273149
2010	3.743885
2011	3.278303
2012	3.690985
2013	4.189328
2014	4.102056
2015	3.109852
2016	3.231096
2017	4.074633
2018	3.004628
2019	3.532025
2020	3.913512
2021	3.537893
2022	4.112946

ggplot(spring_standard_dev_all_408, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 408 average spring temperatures for water years 2005-2021

spring MK & SS for 408 (non-corrected)

spring_sd_mk_408 <- mk.test(spring_standard_dev_all_408$sd_2)
print(spring_sd_mk_408)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_408$sd_2
## z = -0.56758, n = 32, p-value = 0.5703
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -36.00000000 3802.66666667   -0.07258065

spring_sd_sens_408 <- sens.slope(spring_standard_dev_all_408$sd_2)
print(spring_sd_sens_408)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_408$sd_2
## z = -0.56758, n = 32, p-value = 0.5703
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02240538  0.01432186
## sample estimates:
##  Sen's slope 
## -0.003873105

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_408 <- standard_dev_408 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_408 <- fall_standard_dev_all_408 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_408 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	3.768321
1989	2.966066
1990	3.540577
1991	3.633477
1992	5.401512
1995	3.306605
1996	4.289173
1997	4.026644
1998	3.716425
1999	3.326328
2000	3.692913
2001	3.313727
2003	2.672557
2004	4.006060
2005	2.507946
2006	3.743950
2007	3.145367
2008	3.405140
2009	3.230853
2010	3.991380
2011	2.959319
2012	2.942060
2013	3.139594
2014	3.622293
2015	3.127705
2016	2.707995
2017	3.978752
2018	3.563991
2019	3.630854
2020	5.363935
2021	3.926278
2022	3.282654

ggplot(fall_standard_dev_all_408, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 408 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 408 (non-corrected)

fall_sd_mk_408 <- mk.test(fall_standard_dev_all_408$sd_2)
print(fall_sd_mk_408)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_408$sd_2
## z = -0.79461, n = 32, p-value = 0.4268
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -50.0000000 3802.6666667   -0.1008065

fall_sd_sens_408 <- sens.slope(fall_standard_dev_all_408$sd_2)
print(fall_sd_sens_408)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_408$sd_2
## z = -0.79461, n = 32, p-value = 0.4268
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02985931  0.01564404
## sample estimates:
##  Sen's slope 
## -0.005872711

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_408_ad <- standard_dev_408_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_408_ad <- spring_standard_dev_all_408_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_408_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	3.714092
1989	3.852431
1990	2.960315
1991	3.628927
1992	3.065046
1995	2.682351
1996	3.629319
1997	3.811964
1998	2.723386
1999	3.901887
2000	3.959064
2001	3.459362
2003	3.836636
2004	3.510426
2005	3.001941
2006	3.194989
2007	3.569337
2008	3.598630
2009	3.293648
2010	3.756467
2011	3.275085
2012	3.656352
2013	4.218834
2014	4.112872
2015	3.055315
2016	3.214971
2017	4.050030
2018	3.024961
2019	3.480246
2020	3.919687
2021	3.535895
2022	4.103607

ggplot(spring_standard_dev_all_408_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 408 average spring temperatures for water years 1986-2021

spring MK & SS 408 (corrected)

spring_sd_mk_408_ad <- mk.test(spring_standard_dev_all_408_ad$sd_2)
print(spring_sd_mk_408_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_408_ad$sd_2
## z = 0.9892, n = 32, p-value = 0.3226
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##        S     varS      tau 
##   62.000 3802.667    0.125

spring_sd_sens_408_ad <- sens.slope(spring_standard_dev_all_408_ad$sd_2)
print(spring_sd_sens_408_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_408_ad$sd_2
## z = 0.9892, n = 32, p-value = 0.3226
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01076220  0.02557361
## sample estimates:
## Sen's slope 
##  0.01089377

Fall

fall_standard_dev_all_408_ad <- standard_dev_408_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_408_ad <- fall_standard_dev_all_408_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_408_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	3.500114
1989	2.779225
1990	3.190138
1991	3.369412
1992	5.046621
1995	3.013692
1996	3.974926
1997	3.701275
1998	3.344678
1999	3.126846
2000	3.420990
2001	3.033809
2003	2.452351
2004	3.740423
2005	2.316014
2006	3.667225
2007	3.189089
2008	3.348434
2009	3.220502
2010	4.031159
2011	2.936616
2012	2.957996
2013	3.160949
2014	3.642089
2015	3.067864
2016	2.654910
2017	3.931140
2018	3.578413
2019	3.660271
2020	5.431437
2021	3.930767
2022	3.317615

ggplot(fall_standard_dev_all_408_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 408 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 408 (corrected)

fall_sd_mk_408_ad <- mk.test(fall_standard_dev_all_408_ad$sd_2)
print(fall_sd_mk_408_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_408_ad$sd_2
## z = 0.56758, n = 32, p-value = 0.5703
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 3.600000e+01 3.802667e+03 7.258065e-02

fall_sd_sens_408_ad <- sens.slope(fall_standard_dev_all_408_ad$sd_2)
print(fall_sd_sens_408_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_408_ad$sd_2
## z = 0.56758, n = 32, p-value = 0.5703
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01408452  0.02828833
## sample estimates:
## Sen's slope 
## 0.008666756

Columbine Pass 409

Morrisey 6/23/2005

snotel_409 <- SNOTEL_yampa_area %>% 
  filter(site_id == "409")

#str(snotel_409) # check the date, usually a character.  

snotel_409$Date <- as.Date(snotel_409$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_409_clean <- snotel_409 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_409_clean <- snotel_409_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_409_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_409_clean <- snotel_409_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -50) %>% 
  filter(temperature_mean < 40)

ggplot(snotel_409_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_409_cull_count <- snotel_409_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_409_cull_count

# filtering for too few observations in a year
snotel_409_cull_count_days <- snotel_409_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_409_cull_count_days

## # A tibble: 5 x 2
## # Groups:   waterYear [5]
##   waterYear     n
##       <dbl> <int>
## 1      1994   331
## 2      1995   190
## 3      2005   329
## 4      2019   348
## 5      2022   346

snotel_409_clean_culled <- snotel_409_clean %>% 
  filter(waterYear != "1994" & waterYear != "1995" & waterYear != "2005" & waterYear != "2019" & waterYear != "2022")# & waterYear != "1986" & waterYear != "1987" & waterYear != "1994" & waterYear != "2002")# & waterYear != "2002" & waterYear != "2016" & waterYear != "2022")# & waterYear != "2017") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_409_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

ggplot(snotel_409_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_409_xts <- xts(snotel_409_clean_culled$temperature_mean, order.by = snotel_409_clean_culled$Date)

dygraph(temp_409_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

#snotel_409_clean_culled <- snotel_409_clean_culled %>% 
#  filter(temperature_mean > -30)

#temp_409_xts <- xts(snotel_409_clean_culled$temperature_mean, order.by = snotel_409_clean_culled$Date)

#dygraph(temp_409_xts) %>%
#  dyAxis("y", label = "Daily mean temperature (°C)") 

Columbine Pass 409

Morrisey 6/23/2005

snotel_409_adjusted <- snotel_409_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2005-06-23", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

409 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_409 <- snotel_409_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_409 <- yearly_wy_aver_409 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_409 <- daily_wy_aver_409 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_409$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_409 <-daily_wy_aver_409 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_409$date_temp <- signif(daily_wy_aver2_409$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_409, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

409 SD

standard_dev_409 <- daily_wy_aver_409 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

standard_dev_all_409 <- standard_dev_409 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_409 <- standard_dev_all_409 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_409 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.495972
1988	3.864837
1989	4.150756
1990	3.715419
1991	7.886567
1992	3.655020
1993	3.443175
1996	3.871778
1997	3.684240
1998	3.566451
1999	3.690634
2000	3.806945
2001	3.805078
2002	3.935441
2003	3.561320
2004	3.990949
2006	3.799208
2007	3.756201
2008	3.734920
2009	3.575439
2010	3.477648
2011	3.895182
2012	3.326089
2013	3.896199
2014	3.563991
2015	3.704594
2016	3.428127
2017	3.800029
2018	3.317697
2020	3.674904
2021	3.663614

ggplot(standard_dev_all_409, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 409 average temperatures for water years 2005-2021

MK & SS for 409 (non-corrected)

sd_mk_409 <- mk.test(standard_dev_all_409$sd_2)
print(sd_mk_409)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_409$sd_2
## z = -1.5977, n = 31, p-value = 0.1101
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -95.0000000 3461.6666667   -0.2043011

sd_sens_409 <- sens.slope(standard_dev_all_409$sd_2)
print(sd_sens_409)

## 
##  Sen's slope
## 
## data:  standard_dev_all_409$sd_2
## z = -1.5977, n = 31, p-value = 0.1101
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.017215984  0.001425571
## sample estimates:
## Sen's slope 
## -0.00751559

Corrected

409 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_409_ad <- snotel_409_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_409_ad <- yearly_wy_aver_409_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_409_ad <- daily_wy_aver_409_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_409_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_409_ad <-daily_wy_aver_409_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_409_ad$date_temp_ad <- signif(daily_wy_aver2_409_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_409_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

409 SS (corrected)

standard_dev_409_ad <- daily_wy_aver_409_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_409_ad <- standard_dev_409_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_409_ad <- standard_dev_all_409_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_409_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.266770
1988	3.561893
1989	3.882288
1990	3.451808
1991	7.402560
1992	3.437534
1993	3.208576
1996	3.608124
1997	3.447235
1998	3.267783
1999	3.513167
2000	3.521064
2001	3.492918
2002	3.583401
2003	3.261139
2004	3.728286
2006	3.784595
2007	3.779490
2008	3.780985
2009	3.542117
2010	3.511838
2011	3.910483
2012	3.349866
2013	3.931896
2014	3.545831
2015	3.622791
2016	3.429398
2017	3.772145
2018	3.294426
2020	3.730141
2021	3.707606

ggplot(standard_dev_all_409_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 409 average temperatures for water years 1986-2021

MK & SS 409 (corrected)

sd_mk_409_ad <- mk.test(standard_dev_all_409_ad$sd_2)
print(sd_mk_409_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_409_ad$sd_2
## z = 1.2237, n = 31, p-value = 0.221
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   73.0000000 3461.6666667    0.1569892

sd_sens_409_ad <- sens.slope(standard_dev_all_409_ad$sd_2)
print(sd_sens_409_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_409_ad$sd_2
## z = 1.2237, n = 31, p-value = 0.221
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.004188748  0.015233958
## sample estimates:
## Sen's slope 
## 0.006314099

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_409 <- standard_dev_409 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_409 <- summer_standard_dev_all_409 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_409 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.513983
1988	2.371119
1989	2.775714
1990	2.953491
1991	2.526155
1992	2.799705
1993	2.775161
1996	2.038989
1997	2.215588
1998	3.035376
1999	2.307161
2000	2.391550
2001	2.827788
2002	2.559134
2003	2.605412
2004	2.536830
2006	2.418785
2007	1.909282
2008	2.399402
2009	2.273527
2010	2.474689
2011	2.174690
2012	2.004796
2013	2.226754
2014	2.061020
2015	2.530912
2016	2.463450
2017	1.969965
2018	1.809538
2020	2.754058
2021	2.965355

ggplot(summer_standard_dev_all_409, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 409 average summer temperatures for water years 2005-2021

summer MK & SS for 409 (non-corrected)

summer_sd_mk_409 <- mk.test(summer_standard_dev_all_409$sd_2)
print(summer_sd_mk_409)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_409$sd_2
## z = -1.8356, n = 31, p-value = 0.06641
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -109.0000000 3461.6666667   -0.2344086

summer_sd_sens_409 <- sens.slope(summer_standard_dev_all_409$sd_2)
print(summer_sd_sens_409)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_409$sd_2
## z = -1.8356, n = 31, p-value = 0.06641
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.0315290069  0.0007443859
## sample estimates:
## Sen's slope 
## -0.01419181

Winter

winter_standard_dev_all_409 <- standard_dev_409 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_409 <- winter_standard_dev_all_409 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_409 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.000433
1988	4.239064
1989	4.883845
1990	4.233427
1991	9.596274
1992	3.502681
1993	3.733543
1996	4.356658
1997	4.073811
1998	3.812935
1999	3.988981
2000	4.348674
2001	4.040277
2002	4.400388
2003	3.648409
2004	4.635187
2006	4.472151
2007	4.662915
2008	4.406824
2009	4.132535
2010	3.606293
2011	4.927446
2012	3.816428
2013	4.849306
2014	3.804686
2015	4.066909
2016	4.125652
2017	4.352851
2018	4.002004
2020	3.568632
2021	3.928221

ggplot(winter_standard_dev_all_409, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 409 average winter temperatures for water years 2005-2021

winter MK & SS for 409 (non-corrected)

winter_sd_mk_409 <- mk.test(winter_standard_dev_all_409$sd_2)
print(winter_sd_mk_409)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_409$sd_2
## z = -0.54389, n = 31, p-value = 0.5865
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -33.00000000 3461.66666667   -0.07096774

winter_sd_sens_409 <- sens.slope(winter_standard_dev_all_409$sd_2)
print(winter_sd_sens_409)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_409$sd_2
## z = -0.54389, n = 31, p-value = 0.5865
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02394400  0.01553915
## sample estimates:
## Sen's slope 
## -0.00531843

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_409_ad <- standard_dev_409_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_409_ad <- summer_standard_dev_all_409_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_409_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.258912
1988	2.124527
1989	2.475856
1990	2.651125
1991	2.270811
1992	2.507199
1993	2.476143
1996	1.835387
1997	1.983664
1998	2.705591
1999	2.070868
2000	2.154186
2001	2.544216
2002	2.293948
2003	2.318762
2004	2.282365
2006	2.396638
2007	1.920747
2008	2.408611
2009	2.305728
2010	2.463024
2011	2.162252
2012	1.981025
2013	2.204215
2014	2.071051
2015	2.510782
2016	2.447829
2017	1.941966
2018	1.798619
2020	2.749133
2021	2.938145

ggplot(summer_standard_dev_all_409_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 409 average summer temperatures for water years 1986-2021

summer MK & SS 409 (corrected)

summer_sd_mk_409_ad <- mk.test(summer_standard_dev_all_409_ad$sd_2)
print(summer_sd_mk_409_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_409_ad$sd_2
## z = 0, n = 31, p-value = 1
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
## -1.000000e+00  3.461667e+03 -2.150538e-03

summer_sd_sens_409_ad <- sens.slope(summer_standard_dev_all_409_ad$sd_2)
print(summer_sd_sens_409_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_409_ad$sd_2
## z = 0, n = 31, p-value = 1
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01488390  0.01201328
## sample estimates:
##   Sen's slope 
## -0.0001884368

Winter

winter_standard_dev_all_409_ad <- standard_dev_409_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_409_ad <- winter_standard_dev_all_409_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_409_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.830066
1988	4.054246
1989	4.673597
1990	4.017393
1991	8.900135
1992	3.357188
1993	3.578167
1996	4.135939
1997	3.869866
1998	3.633500
1999	3.790833
2000	4.095631
2001	3.875873
2002	4.172906
2003	3.481961
2004	4.412031
2006	4.457990
2007	4.667686
2008	4.422968
2009	4.126597
2010	3.612716
2011	4.919049
2012	3.814114
2013	4.850979
2014	3.795075
2015	4.072789
2016	4.117712
2017	4.362361
2018	3.989836
2020	3.567499
2021	3.917901

ggplot(winter_standard_dev_all_409_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 409 average winter temperatures for water years 1986-2021

winter MK & SS 409 (corrected)

winter_sd_mk_409_ad <- mk.test(winter_standard_dev_all_409_ad$sd_2)
print(winter_sd_mk_409_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_409_ad$sd_2
## z = 0.33993, n = 31, p-value = 0.7339
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 2.100000e+01 3.461667e+03 4.516129e-02

winter_sd_sens_409_ad <- sens.slope(winter_standard_dev_all_409_ad$sd_2)
print(winter_sd_sens_409_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_409_ad$sd_2
## z = 0.33993, n = 31, p-value = 0.7339
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01540047  0.02592081
## sample estimates:
## Sen's slope 
## 0.002927829

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_409 <- standard_dev_409 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_409 <- spring_standard_dev_all_409 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_409 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.561579
1988	4.578729
1989	4.391870
1990	3.208584
1991	6.244185
1992	3.550952
1993	3.582567
1996	4.235865
1997	4.093757
1998	3.351975
1999	4.101267
2000	4.082095
2001	4.245291
2002	3.421203
2003	4.264453
2004	3.528981
2006	3.326359
2007	3.733242
2008	3.651164
2009	3.537388
2010	4.106611
2011	3.726744
2012	3.521956
2013	3.912197
2014	4.235522
2015	3.628131
2016	3.315573
2017	4.173378
2018	3.256959
2020	3.241042
2021	3.286197

ggplot(spring_standard_dev_all_409, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 409 average spring temperatures for water years 2005-2021

spring MK & SS for 409 (non-corrected)

spring_sd_mk_409 <- mk.test(spring_standard_dev_all_409$sd_2)
print(spring_sd_mk_409)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_409$sd_2
## z = -2.0396, n = 31, p-value = 0.04139
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -121.0000000 3461.6666667   -0.2602151

spring_sd_sens_409 <- sens.slope(spring_standard_dev_all_409$sd_2)
print(spring_sd_sens_409)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_409$sd_2
## z = -2.0396, n = 31, p-value = 0.04139
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.0408429507 -0.0009688711
## sample estimates:
## Sen's slope 
## -0.01584774

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_409 <- standard_dev_409 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_409 <- fall_standard_dev_all_409 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_409 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.184045
1988	3.298807
1989	2.587151
1990	3.907058
1991	3.548340
1992	4.252594
1993	3.093285
1996	4.105283
1997	4.033953
1998	3.632605
1999	3.219463
2000	3.691943
2001	3.332071
2002	3.552847
2003	3.322550
2004	4.308047
2006	3.481035
2007	3.175935
2008	3.509452
2009	3.520669
2010	3.763856
2011	2.793876
2012	3.174494
2013	3.108330
2014	3.844918
2015	2.955638
2016	2.674197
2017	3.812446
2018	3.190437
2020	4.956401
2021	4.020098

ggplot(fall_standard_dev_all_409, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 409 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 409 (non-corrected)

fall_sd_mk_409 <- mk.test(fall_standard_dev_all_409$sd_2)
print(fall_sd_mk_409)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_409$sd_2
## z = -0.13597, n = 31, p-value = 0.8918
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##   -9.00000000 3461.66666667   -0.01935484

fall_sd_sens_409 <- sens.slope(fall_standard_dev_all_409$sd_2)
print(fall_sd_sens_409)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_409$sd_2
## z = -0.13597, n = 31, p-value = 0.8918
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02414931  0.02534549
## sample estimates:
##  Sen's slope 
## -0.001612536

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_409_ad <- standard_dev_409_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_409_ad <- spring_standard_dev_all_409_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_409_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.288331
1988	4.193344
1989	4.023275
1990	2.958716
1991	5.715099
1992	3.266312
1993	3.268688
1996	3.843431
1997	3.751459
1998	3.030397
1999	3.753865
2000	3.702838
2001	3.871132
2002	3.112417
2003	3.852353
2004	3.218856
2006	3.329624
2007	3.730793
2008	3.655849
2009	3.566359
2010	4.108949
2011	3.713716
2012	3.506299
2013	3.938093
2014	4.244232
2015	3.573442
2016	3.293115
2017	4.141244
2018	3.279234
2020	3.274358
2021	3.273461

ggplot(spring_standard_dev_all_409_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 409 average spring temperatures for water years 1986-2021

spring MK & SS 409 (corrected)

spring_sd_mk_409_ad <- mk.test(spring_standard_dev_all_409_ad$sd_2)
print(spring_sd_mk_409_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_409_ad$sd_2
## z = -0.30594, n = 31, p-value = 0.7597
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -19.00000000 3461.66666667   -0.04086022

spring_sd_sens_409_ad <- sens.slope(spring_standard_dev_all_409_ad$sd_2)
print(spring_sd_sens_409_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_409_ad$sd_2
## z = -0.30594, n = 31, p-value = 0.7597
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02398139  0.01463308
## sample estimates:
##  Sen's slope 
## -0.003295996

Fall

fall_standard_dev_all_409_ad <- standard_dev_409_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_409_ad <- fall_standard_dev_all_409_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_409_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.907036
1988	3.028108
1989	2.402159
1990	3.499623
1991	3.282029
1992	3.907608
1993	2.842849
1996	3.774849
1997	3.656130
1998	3.269977
1999	2.957556
2000	3.376798
2001	2.963503
2002	3.274083
2003	3.007121
2004	3.967859
2006	3.422927
2007	3.227650
2008	3.470006
2009	3.499157
2010	3.829702
2011	2.802195
2012	3.182752
2013	3.103533
2014	3.880898
2015	2.906173
2016	2.647013
2017	3.757830
2018	3.183640
2020	5.013153
2021	4.037099

ggplot(fall_standard_dev_all_409_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 409 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 409 (corrected)

fall_sd_mk_409_ad <- mk.test(fall_standard_dev_all_409_ad$sd_2)
print(fall_sd_mk_409_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_409_ad$sd_2
## z = 1.1897, n = 31, p-value = 0.2341
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   71.0000000 3461.6666667    0.1526882

fall_sd_sens_409_ad <- sens.slope(fall_standard_dev_all_409_ad$sd_2)
print(fall_sd_sens_409_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_409_ad$sd_2
## z = 1.1897, n = 31, p-value = 0.2341
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.006029522  0.034792793
## sample estimates:
## Sen's slope 
##  0.01375853

Crosho 426

Morrisey 7/21/2005

snotel_426 <- SNOTEL_yampa_area %>% 
  filter(site_id == "426")

#str(snotel_426) # check the date, usually a character.  

snotel_426$Date <- as.Date(snotel_426$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_426_clean <- snotel_426 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_426_clean <- snotel_426_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_426_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_426_clean <- snotel_426_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -50) %>% 
  filter(temperature_mean < 40)

ggplot(snotel_426_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_426_cull_count <- snotel_426_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_426_cull_count

# filtering for too few observations in a year
snotel_426_cull_count_days <- snotel_426_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_426_cull_count_days

## # A tibble: 2 x 2
## # Groups:   waterYear [2]
##   waterYear     n
##       <dbl> <int>
## 1      2009   340
## 2      2021   349

snotel_426_clean_culled <- snotel_426_clean %>% 
  filter(waterYear != "2009" & waterYear != "2021")# & waterYear != "2005" & waterYear != "2019" & waterYear != "2022")# & waterYear != "1986" & waterYear != "1987" & waterYear != "1994" & waterYear != "2002")# & waterYear != "2002" & waterYear != "2016" & waterYear != "2022")# & waterYear != "2017") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_426_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

ggplot(snotel_426_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_426_xts <- xts(snotel_426_clean_culled$temperature_mean, order.by = snotel_426_clean_culled$Date)

dygraph(temp_426_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

#snotel_426_clean_culled <- snotel_426_clean_culled %>% 
#  filter(temperature_mean > -30)

#temp_426_xts <- xts(snotel_426_clean_culled$temperature_mean, order.by = snotel_426_clean_culled$Date)

#dygraph(temp_426_xts) %>%
#  dyAxis("y", label = "Daily mean temperature (°C)") 

Crosho 426 Morrisey 7/21/2005

snotel_426_adjusted <- snotel_426_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2005-07-21", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

426 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_426 <- snotel_426_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_426 <- yearly_wy_aver_426 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_426 <- daily_wy_aver_426 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_426$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_426 <-daily_wy_aver_426 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_426$date_temp <- signif(daily_wy_aver2_426$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_426, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

426 SD

standard_dev_426 <- daily_wy_aver_426 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

standard_dev_all_426 <- standard_dev_426 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_426 <- standard_dev_all_426 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_426 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.835192
1988	6.688853
1989	5.077404
1990	3.898866
1991	4.207908
1992	3.890922
1993	3.892243
1994	3.927671
1995	4.062616
1996	4.066972
1997	4.132857
1998	3.722134
1999	4.072191
2000	3.862336
2001	3.840951
2002	4.151335
2003	3.924485
2004	4.083801
2005	3.670746
2006	4.084252
2007	3.970941
2008	3.872448
2010	3.840234
2011	3.853667
2012	3.626466
2013	4.096949
2014	3.902677
2015	3.917633
2016	3.635992
2017	4.356405
2018	3.785995
2019	3.760199
2020	4.137484
2022	4.114320

ggplot(standard_dev_all_426, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 426 average temperatures for water years 2005-2021

MK & SS for 426 (non-corrected)

sd_mk_426 <- mk.test(standard_dev_all_426$sd_2)
print(sd_mk_426)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_426$sd_2
## z = -1.0674, n = 34, p-value = 0.2858
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -73.0000000 4550.3333333   -0.1301248

sd_sens_426 <- sens.slope(standard_dev_all_426$sd_2)
print(sd_sens_426)

## 
##  Sen's slope
## 
## data:  standard_dev_all_426$sd_2
## z = -1.0674, n = 34, p-value = 0.2858
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01404196  0.00210359
## sample estimates:
##  Sen's slope 
## -0.004490654

Corrected

426 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_426_ad <- snotel_426_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_426_ad <- yearly_wy_aver_426_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_426_ad <- daily_wy_aver_426_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_426_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_426_ad <-daily_wy_aver_426_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_426_ad$date_temp_ad <- signif(daily_wy_aver2_426_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_426_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

426 SS (corrected)

standard_dev_426_ad <- daily_wy_aver_426_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_426_ad <- standard_dev_426_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_426_ad <- standard_dev_all_426_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_426_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.621773
1988	6.284618
1989	4.798125
1990	3.650036
1991	4.006171
1992	3.649429
1993	3.682784
1994	3.639536
1995	3.836511
1996	3.827785
1997	3.903998
1998	3.465023
1999	3.892704
2000	3.618004
2001	3.562946
2002	3.817706
2003	3.637774
2004	3.833913
2005	3.503265
2006	4.089298
2007	4.009181
2008	3.906172
2010	3.883319
2011	3.849569
2012	3.643763
2013	4.135983
2014	3.869632
2015	3.844367
2016	3.641130
2017	4.310487
2018	3.765110
2019	3.792146
2020	4.176947
2022	4.106315

ggplot(standard_dev_all_426_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 426 average temperatures for water years 1986-2021

MK & SS 426 (corrected)

sd_mk_426_ad <- mk.test(standard_dev_all_426_ad$sd_2)
print(sd_mk_426_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_426_ad$sd_2
## z = 1.0377, n = 34, p-value = 0.2994
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   71.0000000 4550.3333333    0.1265597

sd_sens_426_ad <- sens.slope(standard_dev_all_426_ad$sd_2)
print(sd_sens_426_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_426_ad$sd_2
## z = 1.0377, n = 34, p-value = 0.2994
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.003507716  0.013980533
## sample estimates:
## Sen's slope 
## 0.005075351

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_426 <- standard_dev_426 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_426 <- summer_standard_dev_all_426 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_426 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.561915
1988	8.499446
1989	3.193889
1990	3.319147
1991	2.631014
1992	2.935428
1993	3.003495
1994	2.308381
1995	3.481043
1996	1.930165
1997	2.222906
1998	3.038971
1999	2.011450
2000	2.531218
2001	2.872546
2002	2.672038
2003	2.957826
2004	2.829463
2005	2.788555
2006	2.484774
2007	2.241179
2008	2.584209
2010	2.640244
2011	2.091288
2012	2.325230
2013	2.099174
2014	2.271605
2015	2.413969
2016	2.029779
2017	2.172227
2018	2.266581
2019	2.645665
2020	2.827783
2022	2.351090

ggplot(summer_standard_dev_all_426, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 426 average summer temperatures for water years 2005-2021

summer MK & SS for 426 (non-corrected)

summer_sd_mk_426 <- mk.test(summer_standard_dev_all_426$sd_2)
print(summer_sd_mk_426)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_426$sd_2
## z = -2.698, n = 34, p-value = 0.006975
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -183.0000000 4550.3333333   -0.3262032

summer_sd_sens_426 <- sens.slope(summer_standard_dev_all_426$sd_2)
print(summer_sd_sens_426)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_426$sd_2
## z = -2.698, n = 34, p-value = 0.006975
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.038983919 -0.008830423
## sample estimates:
## Sen's slope 
## -0.02505147

Winter

winter_standard_dev_all_426 <- standard_dev_426 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_426 <- winter_standard_dev_all_426 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_426 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.633449
1988	4.588032
1989	5.953397
1990	4.345704
1991	5.099643
1992	3.788197
1993	4.630543
1994	4.681874
1995	4.775390
1996	4.735913
1997	4.840656
1998	4.188165
1999	4.906508
2000	4.310811
2001	4.338845
2002	4.711128
2003	4.404635
2004	4.619416
2005	4.433080
2006	5.090208
2007	4.937391
2008	4.626469
2010	4.277525
2011	4.834824
2012	4.302982
2013	5.134473
2014	4.538643
2015	4.753783
2016	4.563339
2017	5.223504
2018	4.534610
2019	4.308536
2020	4.077340
2022	5.084344

ggplot(winter_standard_dev_all_426, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 426 average winter temperatures for water years 2005-2021

winter MK & SS for 426 (non-corrected)

winter_sd_mk_426 <- mk.test(winter_standard_dev_all_426$sd_2)
print(winter_sd_mk_426)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_426$sd_2
## z = -0.23719, n = 34, p-value = 0.8125
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -17.00000000 4550.33333333   -0.03030303

winter_sd_sens_426 <- sens.slope(winter_standard_dev_all_426$sd_2)
print(winter_sd_sens_426)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_426$sd_2
## z = -0.23719, n = 34, p-value = 0.8125
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.0143643  0.0151971
## sample estimates:
##   Sen's slope 
## -0.0006290057

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_426_ad <- standard_dev_426_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_426_ad <- summer_standard_dev_all_426_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_426_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.304273
1988	7.749827
1989	2.857093
1990	2.981119
1991	2.361494
1992	2.629096
1993	2.694918
1994	2.073101
1995	3.128469
1996	1.728109
1997	2.001086
1998	2.714173
1999	1.796497
2000	2.278366
2001	2.586670
2002	2.395018
2003	2.626229
2004	2.542632
2005	2.542724
2006	2.462350
2007	2.265665
2008	2.605594
2010	2.630546
2011	2.078277
2012	2.306938
2013	2.078865
2014	2.264114
2015	2.385749
2016	2.019871
2017	2.152222
2018	2.260432
2019	2.654388
2020	2.818208
2022	2.332766

ggplot(summer_standard_dev_all_426_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 426 average summer temperatures for water years 1986-2021

summer MK & SS 426 (corrected)

summer_sd_mk_426_ad <- mk.test(summer_standard_dev_all_426_ad$sd_2)
print(summer_sd_mk_426_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_426_ad$sd_2
## z = -1.4528, n = 34, p-value = 0.1463
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -99.0000000 4550.3333333   -0.1764706

summer_sd_sens_426_ad <- sens.slope(summer_standard_dev_all_426_ad$sd_2)
print(summer_sd_sens_426_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_426_ad$sd_2
## z = -1.4528, n = 34, p-value = 0.1463
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02470744  0.00301763
## sample estimates:
## Sen's slope 
## -0.01106122

Winter

winter_standard_dev_all_426_ad <- standard_dev_426_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_426_ad <- winter_standard_dev_all_426_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_426_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.483793
1988	4.439307
1989	5.766238
1990	4.174383
1991	4.999735
1992	3.658075
1993	4.496106
1994	4.523864
1995	4.575988
1996	4.540164
1997	4.634909
1998	4.020920
1999	4.705789
2000	4.099080
2001	4.201343
2002	4.515914
2003	4.224457
2004	4.407266
2005	4.278418
2006	5.082393
2007	4.949550
2008	4.638489
2010	4.279362
2011	4.830591
2012	4.305814
2013	5.132933
2014	4.530534
2015	4.751074
2016	4.556741
2017	5.241161
2018	4.524075
2019	4.290539
2020	4.079926
2022	5.080857

ggplot(winter_standard_dev_all_426_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 426 average winter temperatures for water years 1986-2021

winter MK & SS 426 (corrected)

winter_sd_mk_426_ad <- mk.test(winter_standard_dev_all_426_ad$sd_2)
print(winter_sd_mk_426_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_426_ad$sd_2
## z = 1.1563, n = 34, p-value = 0.2476
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##          S       varS        tau 
##   79.00000 4550.33333    0.14082

winter_sd_sens_426_ad <- sens.slope(winter_standard_dev_all_426_ad$sd_2)
print(winter_sd_sens_426_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_426_ad$sd_2
## z = 1.1563, n = 34, p-value = 0.2476
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.008076346  0.021657462
## sample estimates:
## Sen's slope 
## 0.006342779

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_426 <- standard_dev_426 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_426 <- spring_standard_dev_all_426 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_426 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.837405
1988	4.288258
1989	4.654485
1990	3.561537
1991	4.304889
1992	3.588578
1993	3.164816
1994	3.522606
1995	3.125270
1996	4.151544
1997	4.227277
1998	3.192372
1999	4.073256
2000	4.488816
2001	3.615185
2002	3.529639
2003	4.314043
2004	3.931816
2005	3.409760
2006	3.327158
2007	3.723713
2008	3.842827
2010	3.776037
2011	3.587523
2012	3.811585
2013	4.016637
2014	4.369561
2015	3.236788
2016	3.274070
2017	4.087448
2018	3.291429
2019	3.667254
2020	3.834066
2022	4.327015

ggplot(spring_standard_dev_all_426, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 426 average spring temperatures for water years 2005-2021

spring MK & SS for 426 (non-corrected)

spring_sd_mk_426 <- mk.test(spring_standard_dev_all_426$sd_2)
print(spring_sd_mk_426)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_426$sd_2
## z = -0.26684, n = 34, p-value = 0.7896
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -19.00000000 4550.33333333   -0.03386809

spring_sd_sens_426 <- sens.slope(spring_standard_dev_all_426$sd_2)
print(spring_sd_sens_426)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_426$sd_2
## z = -0.26684, n = 34, p-value = 0.7896
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02100139  0.01296933
## sample estimates:
##  Sen's slope 
## -0.004355336

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_426 <- standard_dev_426 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_426 <- fall_standard_dev_all_426 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_426 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.884732
1988	6.745804
1989	5.096664
1990	3.775418
1991	3.524701
1992	4.680895
1993	3.530917
1994	3.064101
1995	3.208967
1996	4.362177
1997	4.275355
1998	3.827847
1999	3.256104
2000	3.654246
2001	3.162884
2002	3.633691
2003	3.229079
2004	4.099131
2005	2.748810
2006	3.662911
2007	3.392219
2008	3.266605
2010	4.221162
2011	2.959640
2012	3.068566
2013	3.345301
2014	3.454693
2015	3.147744
2016	2.862284
2017	4.092287
2018	3.839550
2019	3.731957
2020	5.555161
2022	2.845616

ggplot(fall_standard_dev_all_426, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 426 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 426 (non-corrected)

fall_sd_mk_426 <- mk.test(fall_standard_dev_all_426$sd_2)
print(fall_sd_mk_426)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_426$sd_2
## z = -1.3046, n = 34, p-value = 0.192
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -89.0000000 4550.3333333   -0.1586453

fall_sd_sens_426 <- sens.slope(fall_standard_dev_all_426$sd_2)
print(fall_sd_sens_426)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_426$sd_2
## z = -1.3046, n = 34, p-value = 0.192
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.04464689  0.00921403
## sample estimates:
## Sen's slope 
## -0.01762082

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_426_ad <- standard_dev_426_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_426_ad <- spring_standard_dev_all_426_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_426_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.532429
1988	3.957866
1989	4.264430
1990	3.300775
1991	3.979192
1992	3.301636
1993	2.893470
1994	3.198425
1995	2.910820
1996	3.810213
1997	3.919848
1998	2.887783
1999	3.757543
2000	4.091753
2001	3.302349
2002	3.225349
2003	3.921561
2004	3.595824
2005	3.112766
2006	3.317861
2007	3.716677
2008	3.880227
2010	3.784323
2011	3.575653
2012	3.773875
2013	4.046846
2014	4.375575
2015	3.174395
2016	3.247170
2017	4.061459
2018	3.317316
2019	3.608775
2020	3.846988
2022	4.320131

ggplot(spring_standard_dev_all_426_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 426 average spring temperatures for water years 1986-2021

spring MK & SS 426 (corrected)

spring_sd_mk_426_ad <- mk.test(spring_standard_dev_all_426_ad$sd_2)
print(spring_sd_mk_426_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_426_ad$sd_2
## z = 1.097, n = 34, p-value = 0.2726
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   75.0000000 4550.3333333    0.1336898

spring_sd_sens_426_ad <- sens.slope(spring_standard_dev_all_426_ad$sd_2)
print(spring_sd_sens_426_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_426_ad$sd_2
## z = 1.097, n = 34, p-value = 0.2726
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.007517419  0.025435829
## sample estimates:
## Sen's slope 
##   0.0086748

Fall

fall_standard_dev_all_426_ad <- standard_dev_426_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_426_ad <- fall_standard_dev_all_426_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_426_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.639893
1988	6.314365
1989	4.662097
1990	3.411545
1991	3.240440
1992	4.323651
1993	3.260763
1994	2.760201
1995	2.908277
1996	4.008820
1997	3.913482
1998	3.465670
1999	3.014203
2000	3.341717
2001	2.849709
2002	3.333744
2003	2.931703
2004	3.786224
2005	2.520289
2006	3.612694
2007	3.443398
2008	3.217693
2010	4.263348
2011	2.950439
2012	3.086710
2013	3.352698
2014	3.483170
2015	3.099394
2016	2.831106
2017	4.047741
2018	3.866223
2019	3.776151
2020	5.617925
2022	2.875449

ggplot(fall_standard_dev_all_426_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 426 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 426 (corrected)

fall_sd_mk_426_ad <- mk.test(fall_standard_dev_all_426_ad$sd_2)
print(fall_sd_mk_426_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_426_ad$sd_2
## z = -0.029649, n = 34, p-value = 0.9763
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
## -3.000000e+00  4.550333e+03 -5.347594e-03

fall_sd_sens_426_ad <- sens.slope(fall_standard_dev_all_426_ad$sd_2)
print(fall_sd_sens_426_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_426_ad$sd_2
## z = -0.029649, n = 34, p-value = 0.9763
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02782460  0.02261001
## sample estimates:
##  Sen's slope 
## -0.001313105

Dry Lake 457

Oyler -> Morrisey 7/30/2003

snotel_457 <- SNOTEL_yampa_area %>% 
  filter(site_id == "457")

#str(snotel_457) # check the date, usually a character.  

snotel_457$Date <- as.Date(snotel_457$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_457_clean <- snotel_457 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_457_clean <- snotel_457_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_457_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_457_clean <- snotel_457_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -40) %>% 
  filter(temperature_mean < 40)

ggplot(snotel_457_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_457_cull_count <- snotel_457_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_457_cull_count

# filtering for too few observations in a year
snotel_457_cull_count_days <- snotel_457_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_457_cull_count_days

## # A tibble: 6 x 2
## # Groups:   waterYear [6]
##   waterYear     n
##       <dbl> <int>
## 1      1985     1
## 2      1994   332
## 3      1996   349
## 4      1997   329
## 5      2003   346
## 6      2021   346

snotel_457_clean_culled <- snotel_457_clean %>% 
  filter(waterYear != "1985" & waterYear != "1986" & waterYear != "1994" & waterYear != "1996" & waterYear != "1997" & waterYear != "2003" & waterYear != "2021")# & waterYear != "1987" & waterYear != "1994" & waterYear != "2002")# & waterYear != "2002" & waterYear != "2016" & waterYear != "2022")# & waterYear != "2017") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_457_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Also 1986

ggplot(snotel_457_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_457_xts <- xts(snotel_457_clean_culled$temperature_mean, order.by = snotel_457_clean_culled$Date)

dygraph(temp_457_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

#snotel_457_clean_culled <- snotel_457_clean_culled %>% 
#  filter(temperature_mean > -30)

#temp_457_xts <- xts(snotel_457_clean_culled$temperature_mean, order.by = snotel_457_clean_culled$Date)

#dygraph(temp_457_xts) %>%
#  dyAxis("y", label = "Daily mean temperature (°C)") 

Dry Lake 457 Oyler -> Morrisey 7/30/2003

snotel_457_adjusted <- snotel_457_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2003-07-30", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

457 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_457 <- snotel_457_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_457 <- yearly_wy_aver_457 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_457 <- daily_wy_aver_457 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_457$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_457 <-daily_wy_aver_457 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_457$date_temp <- signif(daily_wy_aver2_457$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_457, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

457 SD

standard_dev_457 <- daily_wy_aver_457 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

standard_dev_all_457 <- standard_dev_457 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_457 <- standard_dev_all_457 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_457 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.884974
1988	4.014791
1989	4.324895
1990	3.800111
1991	4.038363
1992	3.821326
1993	5.722207
1995	3.778895
1998	3.555486
1999	3.819029
2000	3.591974
2001	3.729893
2002	3.884897
2004	3.709982
2005	3.472614
2006	3.707982
2007	3.751542
2008	3.519945
2009	3.665004
2010	3.648463
2011	3.766168
2012	3.370437
2013	3.973797
2014	3.519003
2015	3.799974
2016	3.312714
2017	4.001117
2018	3.383327
2019	3.471526
2020	4.040049
2022	3.803178

ggplot(standard_dev_all_457, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 457 average temperatures for water years 2005-2021

MK & SS for 457 (non-corrected)

sd_mk_457 <- mk.test(standard_dev_all_457$sd_2)
print(sd_mk_457)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_457$sd_2
## z = -2.3455, n = 31, p-value = 0.019
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -139.0000000 3461.6666667   -0.2989247

sd_sens_457 <- sens.slope(standard_dev_all_457$sd_2)
print(sd_sens_457)

## 
##  Sen's slope
## 
## data:  standard_dev_all_457$sd_2
## z = -2.3455, n = 31, p-value = 0.019
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.021914907 -0.001270345
## sample estimates:
## Sen's slope 
## -0.01272964

Corrected

457 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_457_ad <- snotel_457_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_457_ad <- yearly_wy_aver_457_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_457_ad <- daily_wy_aver_457_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_457_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_457_ad <-daily_wy_aver_457_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_457_ad$date_temp_ad <- signif(daily_wy_aver2_457_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_457_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

457 SS (corrected)

standard_dev_457_ad <- daily_wy_aver_457_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_457_ad <- standard_dev_457_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_457_ad <- standard_dev_all_457_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_457_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.645348
1988	3.665185
1989	4.055607
1990	3.513014
1991	3.810883
1992	3.622286
1993	5.419071
1995	3.589615
1998	3.299813
1999	3.655912
2000	3.355427
2001	3.415352
2002	3.542588
2004	3.656210
2005	3.423205
2006	3.717944
2007	3.782830
2008	3.548199
2009	3.611844
2010	3.649976
2011	3.761584
2012	3.393902
2013	4.006266
2014	3.500715
2015	3.734459
2016	3.316833
2017	3.963337
2018	3.367592
2019	3.483300
2020	4.062368
2022	3.788996

ggplot(standard_dev_all_457_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 457 average temperatures for water years 1986-2021

MK & SS 457 (corrected)

sd_mk_457_ad <- mk.test(standard_dev_all_457_ad$sd_2)
print(sd_mk_457_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_457_ad$sd_2
## z = 0.067986, n = 31, p-value = 0.9458
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 5.000000e+00 3.461667e+03 1.075269e-02

sd_sens_457_ad <- sens.slope(standard_dev_all_457_ad$sd_2)
print(sd_sens_457_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_457_ad$sd_2
## z = 0.067986, n = 31, p-value = 0.9458
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.009521827  0.010854648
## sample estimates:
##  Sen's slope 
## 0.0002504338

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_457 <- standard_dev_457 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_457 <- summer_standard_dev_all_457 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_457 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.715034
1988	2.556229
1989	2.993638
1990	3.686055
1991	2.675449
1992	2.972210
1993	3.821814
1995	3.172156
1998	3.114769
1999	1.879389
2000	2.581509
2001	2.869486
2002	2.674083
2004	2.636336
2005	2.843564
2006	2.458939
2007	2.268531
2008	2.618322
2009	2.248735
2010	2.226268
2011	2.050133
2012	2.231663
2013	2.089620
2014	2.342618
2015	2.438775
2016	2.188310
2017	2.048909
2018	2.267535
2019	2.459158
2020	2.778913
2022	2.356948

ggplot(summer_standard_dev_all_457, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 457 average summer temperatures for water years 2005-2021

summer MK & SS for 457 (non-corrected)

summer_sd_mk_457 <- mk.test(summer_standard_dev_all_457$sd_2)
print(summer_sd_mk_457)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_457$sd_2
## z = -3.3993, n = 31, p-value = 0.0006756
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -201.0000000 3461.6666667   -0.4322581

summer_sd_sens_457 <- sens.slope(summer_standard_dev_all_457$sd_2)
print(summer_sd_sens_457)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_457$sd_2
## z = -3.3993, n = 31, p-value = 0.0006756
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.04396671 -0.01225003
## sample estimates:
## Sen's slope 
## -0.02663665

Winter

winter_standard_dev_all_457 <- standard_dev_457 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_457 <- winter_standard_dev_all_457 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_457 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.388486
1988	4.308822
1989	5.245875
1990	3.929205
1991	4.800144
1992	3.879404
1993	4.066957
1995	4.417012
1998	3.983577
1999	4.481958
2000	3.757025
2001	4.045222
2002	4.314290
2004	4.045809
2005	4.060581
2006	4.433084
2007	4.570095
2008	3.975320
2009	4.290873
2010	4.067131
2011	4.690569
2012	3.919100
2013	4.790811
2014	3.885731
2015	4.599394
2016	3.952992
2017	4.710055
2018	3.922943
2019	4.013772
2020	3.757616
2022	4.510978

ggplot(winter_standard_dev_all_457, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 457 average winter temperatures for water years 2005-2021

winter MK & SS for 457 (non-corrected)

winter_sd_mk_457 <- mk.test(winter_standard_dev_all_457$sd_2)
print(winter_sd_mk_457)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_457$sd_2
## z = -0.50989, n = 31, p-value = 0.6101
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -31.00000000 3461.66666667   -0.06666667

winter_sd_sens_457 <- sens.slope(winter_standard_dev_all_457$sd_2)
print(winter_sd_sens_457)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_457$sd_2
## z = -0.50989, n = 31, p-value = 0.6101
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01920191  0.01092712
## sample estimates:
##  Sen's slope 
## -0.003902823

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_457_ad <- standard_dev_457_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_457_ad <- summer_standard_dev_all_457_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_457_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.440975
1988	2.317422
1989	2.661004
1990	3.320028
1991	2.414911
1992	2.671853
1993	3.454838
1995	2.847482
1998	2.761645
1999	1.677913
2000	2.322446
2001	2.579485
2002	2.400801
2004	2.620217
2005	2.881576
2006	2.437167
2007	2.293169
2008	2.639301
2009	2.255995
2010	2.217062
2011	2.051982
2012	2.212844
2013	2.068541
2014	2.338613
2015	2.407117
2016	2.157603
2017	2.027620
2018	2.255235
2019	2.471745
2020	2.764237
2022	2.343038

ggplot(summer_standard_dev_all_457_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 457 average summer temperatures for water years 1986-2021

summer MK & SS 457 (corrected)

summer_sd_mk_457_ad <- mk.test(summer_standard_dev_all_457_ad$sd_2)
print(summer_sd_mk_457_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_457_ad$sd_2
## z = -2.2775, n = 31, p-value = 0.02276
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -135.0000000 3461.6666667   -0.2903226

summer_sd_sens_457_ad <- sens.slope(summer_standard_dev_all_457_ad$sd_2)
print(summer_sd_sens_457_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_457_ad$sd_2
## z = -2.2775, n = 31, p-value = 0.02276
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.027046391 -0.002712733
## sample estimates:
## Sen's slope 
## -0.01381021

Winter

winter_standard_dev_all_457_ad <- standard_dev_457_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_457_ad <- winter_standard_dev_all_457_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_457_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.228054
1988	4.141521
1989	5.089489
1990	3.759066
1991	4.696255
1992	3.733794
1993	3.909935
1995	4.233399
1998	3.838113
1999	4.324385
2000	3.575518
2001	3.916584
2002	4.144328
2004	4.050383
2005	4.044804
2006	4.432058
2007	4.579749
2008	3.984739
2009	4.282469
2010	4.069145
2011	4.686978
2012	3.914672
2013	4.789729
2014	3.881118
2015	4.593943
2016	3.945343
2017	4.722885
2018	3.911439
2019	4.002148
2020	3.754267
2022	4.507667

ggplot(winter_standard_dev_all_457_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 457 average winter temperatures for water years 1986-2021

winter MK & SS 457 (corrected)

winter_sd_mk_457_ad <- mk.test(winter_standard_dev_all_457_ad$sd_2)
print(winter_sd_mk_457_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_457_ad$sd_2
## z = 0.30594, n = 31, p-value = 0.7597
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 1.900000e+01 3.461667e+03 4.086022e-02

winter_sd_sens_457_ad <- sens.slope(winter_standard_dev_all_457_ad$sd_2)
print(winter_sd_sens_457_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_457_ad$sd_2
## z = 0.30594, n = 31, p-value = 0.7597
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01437935  0.02006409
## sample estimates:
## Sen's slope 
## 0.001863624

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_457 <- standard_dev_457 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_457 <- spring_standard_dev_all_457 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_457 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.386031
1988	4.459451
1989	3.822866
1990	3.299009
1991	4.009404
1992	3.411259
1993	3.046514
1995	2.670175
1998	2.841989
1999	4.227073
2000	4.087119
2001	3.318495
2002	3.298014
2004	3.638133
2005	3.183624
2006	3.143637
2007	3.588017
2008	3.440174
2009	3.243501
2010	3.847503
2011	3.265820
2012	3.617653
2013	4.133515
2014	3.824506
2015	3.048643
2016	3.003636
2017	4.042746
2018	3.129144
2019	3.355311
2020	3.890975
2022	3.991301

ggplot(spring_standard_dev_all_457, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 457 average spring temperatures for water years 2005-2021

spring MK & SS for 457 (non-corrected)

spring_sd_mk_457 <- mk.test(spring_standard_dev_all_457$sd_2)
print(spring_sd_mk_457)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_457$sd_2
## z = -0.44191, n = 31, p-value = 0.6586
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -27.00000000 3461.66666667   -0.05806452

spring_sd_sens_457 <- sens.slope(spring_standard_dev_all_457$sd_2)
print(spring_sd_sens_457)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_457$sd_2
## z = -0.44191, n = 31, p-value = 0.6586
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02441413  0.02027985
## sample estimates:
##  Sen's slope 
## -0.005749092

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_457 <- standard_dev_457 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_457 <- fall_standard_dev_all_457 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_457 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.258978
1988	3.335103
1989	3.043591
1990	3.937161
1991	3.601756
1992	4.285951
1993	10.491729
1995	3.297522
1998	3.565366
1999	3.419214
2000	3.873739
2001	3.250979
2002	3.286525
2004	3.705007
2005	2.337545
2006	3.556737
2007	3.230608
2008	3.363509
2009	3.376364
2010	4.016771
2011	2.997267
2012	2.868907
2013	3.563170
2014	3.642415
2015	3.141705
2016	2.818319
2017	3.782320
2018	3.503160
2019	3.384743
2020	5.610141
2022	3.205941

ggplot(fall_standard_dev_all_457, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 457 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 457 (non-corrected)

fall_sd_mk_457 <- mk.test(fall_standard_dev_all_457$sd_2)
print(fall_sd_mk_457)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_457$sd_2
## z = -0.61187, n = 31, p-value = 0.5406
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -37.00000000 3461.66666667   -0.07956989

fall_sd_sens_457 <- sens.slope(fall_standard_dev_all_457$sd_2)
print(fall_sd_sens_457)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_457$sd_2
## z = -0.61187, n = 31, p-value = 0.5406
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02398242  0.01396515
## sample estimates:
##  Sen's slope 
## -0.004464742

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_457_ad <- standard_dev_457_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_457_ad <- spring_standard_dev_all_457_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_457_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.010234
1988	4.063885
1989	3.477151
1990	3.040868
1991	3.641795
1992	3.134867
1993	2.752124
1995	2.493756
1998	2.559476
1999	3.886270
2000	3.725227
2001	3.027271
2002	2.999060
2004	3.609415
2005	3.189020
2006	3.137605
2007	3.590867
2008	3.469474
2009	3.270375
2010	3.848606
2011	3.245933
2012	3.590219
2013	4.163119
2014	3.836515
2015	3.008115
2016	2.986892
2017	4.020390
2018	3.164311
2019	3.309858
2020	3.913199
2022	3.982235

ggplot(spring_standard_dev_all_457_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 457 average spring temperatures for water years 1986-2021

spring MK & SS 457 (corrected)

spring_sd_mk_457_ad <- mk.test(spring_standard_dev_all_457_ad$sd_2)
print(spring_sd_mk_457_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_457_ad$sd_2
## z = 0.88381, n = 31, p-value = 0.3768
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   53.0000000 3461.6666667    0.1139785

spring_sd_sens_457_ad <- sens.slope(spring_standard_dev_all_457_ad$sd_2)
print(spring_sd_sens_457_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_457_ad$sd_2
## z = 0.88381, n = 31, p-value = 0.3768
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01178487  0.03389473
## sample estimates:
## Sen's slope 
##  0.01042372

Fall

fall_standard_dev_all_457_ad <- standard_dev_457_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_457_ad <- fall_standard_dev_all_457_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_457_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.989854
1988	3.047028
1989	2.809749
1990	3.500073
1991	3.282132
1992	3.956609
1993	9.897354
1995	2.962855
1998	3.147154
1999	3.196750
2000	3.546844
2001	2.928983
2002	3.006940
2004	3.661237
2005	2.354633
2006	3.516974
2007	3.273133
2008	3.330535
2009	3.386184
2010	4.041544
2011	3.000260
2012	2.907570
2013	3.591512
2014	3.673234
2015	3.108161
2016	2.786871
2017	3.757872
2018	3.527010
2019	3.427057
2020	5.666724
2022	3.232635

ggplot(fall_standard_dev_all_457_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 457 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 457 (corrected)

fall_sd_mk_457_ad <- mk.test(fall_standard_dev_all_457_ad$sd_2)
print(fall_sd_mk_457_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_457_ad$sd_2
## z = 1.1897, n = 31, p-value = 0.2341
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   71.0000000 3461.6666667    0.1526882

fall_sd_sens_457_ad <- sens.slope(fall_standard_dev_all_457_ad$sd_2)
print(fall_sd_sens_457_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_457_ad$sd_2
## z = 1.1897, n = 31, p-value = 0.2341
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.007747232  0.029712171
## sample estimates:
## Sen's slope 
##  0.01172958

Elk River 467

Oyler -> Morrisey 8/7/2006

snotel_467 <- SNOTEL_yampa_area %>% 
  filter(site_id == "467")

#str(snotel_467) # check the date, usually a character.  

snotel_467$Date <- as.Date(snotel_467$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_467_clean <- snotel_467 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_467_clean <- snotel_467_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_467_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_467_clean <- snotel_467_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -40) %>% 
  filter(temperature_mean < 40)

ggplot(snotel_467_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_467_cull_count <- snotel_467_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_467_cull_count

# filtering for too few observations in a year
snotel_467_cull_count_days <- snotel_467_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_467_cull_count_days

## # A tibble: 6 x 2
## # Groups:   waterYear [6]
##   waterYear     n
##       <dbl> <int>
## 1      1985     1
## 2      1994   326
## 3      1998   342
## 4      1999   281
## 5      2001   339
## 6      2021   344

snotel_467_clean_culled <- snotel_467_clean %>% 
  filter(waterYear != "1985" & waterYear != "1986" & waterYear != "1994" & waterYear != "1998" & waterYear != "1999" & waterYear != "2001" & waterYear != "2021")# & waterYear != "2021")# & waterYear != "1987" & waterYear != "1994" & waterYear != "2002")# & waterYear != "2002" & waterYear != "2016" & waterYear != "2022")# & waterYear != "2017") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_467_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Also 1986

ggplot(snotel_467_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_467_xts <- xts(snotel_467_clean_culled$temperature_mean, order.by = snotel_467_clean_culled$Date)

dygraph(temp_467_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

#snotel_467_clean_culled <- snotel_467_clean_culled %>% 
#  filter(temperature_mean > -30)

#temp_467_xts <- xts(snotel_467_clean_culled$temperature_mean, order.by = snotel_467_clean_culled$Date)

#dygraph(temp_467_xts) %>%
#  dyAxis("y", label = "Daily mean temperature (°C)") 

Elk River 467 Oyler -> Morrisey 8/7/2006

snotel_467_adjusted <- snotel_467_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2006-08-07", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

467 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_467 <- snotel_467_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_467 <- yearly_wy_aver_467 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_467 <- daily_wy_aver_467 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_467$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_467 <-daily_wy_aver_467 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_467$date_temp <- signif(daily_wy_aver2_467$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_467, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

467 SD

standard_dev_467 <- daily_wy_aver_467 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

standard_dev_all_467 <- standard_dev_467 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_467 <- standard_dev_all_467 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_467 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.145999
1988	4.540989
1989	4.813588
1990	4.099732
1991	4.399539
1992	4.337342
1993	4.115276
1995	4.206810
1996	4.099000
1997	4.118831
2000	4.115022
2002	4.236140
2003	3.935416
2004	4.252626
2005	3.710645
2006	4.277168
2007	4.029093
2008	3.866990
2009	4.006806
2010	3.899850
2011	3.849996
2012	3.715984
2013	4.270444
2014	3.899404
2015	4.163138
2016	3.597994
2017	4.347721
2018	3.730401
2019	3.749406
2020	4.233462
2022	4.158564

ggplot(standard_dev_all_467, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 467 average temperatures for water years 2005-2021

MK & SS for 467 (non-corrected)

sd_mk_467 <- mk.test(standard_dev_all_467$sd_2)
print(sd_mk_467)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_467$sd_2
## z = -2.5495, n = 31, p-value = 0.01079
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -151.0000000 3461.6666667   -0.3247312

sd_sens_467 <- sens.slope(standard_dev_all_467$sd_2)
print(sd_sens_467)

## 
##  Sen's slope
## 
## data:  standard_dev_all_467$sd_2
## z = -2.5495, n = 31, p-value = 0.01079
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02661947 -0.00432832
## sample estimates:
## Sen's slope 
## -0.01539253

Corrected

467 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_467_ad <- snotel_467_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_467_ad <- yearly_wy_aver_467_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_467_ad <- daily_wy_aver_467_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_467_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_467_ad <-daily_wy_aver_467_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_467_ad$date_temp_ad <- signif(daily_wy_aver2_467_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_467_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

467 SS (corrected)

standard_dev_467_ad <- daily_wy_aver_467_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_467_ad <- standard_dev_467_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_467_ad <- standard_dev_all_467_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_467_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.897877
1988	4.166810
1989	4.517446
1990	3.809051
1991	4.164976
1992	4.101268
1993	3.862819
1995	3.991982
1996	3.869998
1997	3.891711
2000	3.849542
2002	3.910714
2003	3.658870
2004	4.024479
2005	3.518339
2006	4.066730
2007	4.047461
2008	3.891100
2009	3.935836
2010	3.903805
2011	3.848928
2012	3.730038
2013	4.302517
2014	3.867339
2015	4.080572
2016	3.593402
2017	4.299547
2018	3.703800
2019	3.767250
2020	4.265659
2022	4.152731

ggplot(standard_dev_all_467_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 467 average temperatures for water years 1986-2021

MK & SS 467 (corrected)

sd_mk_467_ad <- mk.test(standard_dev_all_467_ad$sd_2)
print(sd_mk_467_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_467_ad$sd_2
## z = -0.61187, n = 31, p-value = 0.5406
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -37.00000000 3461.66666667   -0.07956989

sd_sens_467_ad <- sens.slope(standard_dev_all_467_ad$sd_2)
print(sd_sens_467_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_467_ad$sd_2
## z = -0.61187, n = 31, p-value = 0.5406
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.013472791  0.006773726
## sample estimates:
##  Sen's slope 
## -0.003319246

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_467 <- standard_dev_467 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_467 <- summer_standard_dev_all_467 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_467 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.951866
1988	3.122046
1989	3.666727
1990	3.496364
1991	2.501052
1992	3.228632
1993	3.962014
1995	3.474405
1996	2.019638
1997	2.426146
2000	2.883427
2002	2.872409
2003	3.265097
2004	3.042612
2005	3.343196
2006	2.912617
2007	2.468128
2008	3.026408
2009	2.538826
2010	2.436467
2011	2.274045
2012	2.404012
2013	2.450505
2014	2.598154
2015	2.694083
2016	2.326506
2017	2.378353
2018	2.494011
2019	2.687749
2020	2.839960
2022	2.460476

ggplot(summer_standard_dev_all_467, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 467 average summer temperatures for water years 2005-2021

summer MK & SS for 467 (non-corrected)

summer_sd_mk_467 <- mk.test(summer_standard_dev_all_467$sd_2)
print(summer_sd_mk_467)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_467$sd_2
## z = -2.8894, n = 31, p-value = 0.00386
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -171.0000000 3461.6666667   -0.3677419

summer_sd_sens_467 <- sens.slope(summer_standard_dev_all_467$sd_2)
print(summer_sd_sens_467)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_467$sd_2
## z = -2.8894, n = 31, p-value = 0.00386
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.044445765 -0.008302021
## sample estimates:
## Sen's slope 
##  -0.0256963

Winter

winter_standard_dev_all_467 <- standard_dev_467 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_467 <- winter_standard_dev_all_467 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_467 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.807249
1988	4.695919
1989	5.557602
1990	4.423012
1991	5.187413
1992	4.318765
1993	4.397918
1995	4.732098
1996	4.765163
1997	4.722889
2000	4.400274
2002	4.741924
2003	4.240216
2004	4.647977
2005	4.222899
2006	5.007043
2007	4.902428
2008	4.293852
2009	4.672422
2010	4.238347
2011	4.686434
2012	4.348109
2013	5.172502
2014	4.250876
2015	5.003587
2016	4.322953
2017	5.011875
2018	4.311699
2019	4.300647
2020	3.912165
2022	4.887383

ggplot(winter_standard_dev_all_467, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 467 average winter temperatures for water years 2005-2021

winter MK & SS for 467 (non-corrected)

winter_sd_mk_467 <- mk.test(winter_standard_dev_all_467$sd_2)
print(winter_sd_mk_467)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_467$sd_2
## z = -1.4277, n = 31, p-value = 0.1534
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -85.0000000 3461.6666667   -0.1827957

winter_sd_sens_467 <- sens.slope(winter_standard_dev_all_467$sd_2)
print(winter_sd_sens_467)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_467$sd_2
## z = -1.4277, n = 31, p-value = 0.1534
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.024019831  0.004144003
## sample estimates:
##  Sen's slope 
## -0.007746222

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_467_ad <- standard_dev_467_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_467_ad <- summer_standard_dev_all_467_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_467_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.661099
1988	2.813713
1989	3.272530
1990	3.144473
1991	2.248762
1992	2.904015
1993	3.572050
1995	3.119035
1996	1.823712
1997	2.185937
2000	2.594429
2002	2.579701
2003	2.891295
2004	2.744692
2005	2.972598
2006	2.699705
2007	2.482490
2008	3.042267
2009	2.557233
2010	2.435837
2011	2.267432
2012	2.372337
2013	2.421113
2014	2.594249
2015	2.646408
2016	2.293848
2017	2.349915
2018	2.485827
2019	2.706459
2020	2.828304
2022	2.453579

ggplot(summer_standard_dev_all_467_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 467 average summer temperatures for water years 1986-2021

summer MK & SS 467 (corrected)

summer_sd_mk_467_ad <- mk.test(summer_standard_dev_all_467_ad$sd_2)
print(summer_sd_mk_467_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_467_ad$sd_2
## z = -1.8356, n = 31, p-value = 0.06641
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -109.0000000 3461.6666667   -0.2344086

summer_sd_sens_467_ad <- sens.slope(summer_standard_dev_all_467_ad$sd_2)
print(summer_sd_sens_467_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_467_ad$sd_2
## z = -1.8356, n = 31, p-value = 0.06641
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.027031212  0.001166882
## sample estimates:
## Sen's slope 
## -0.01469003

Winter

winter_standard_dev_all_467_ad <- standard_dev_467_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_467_ad <- winter_standard_dev_all_467_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_467_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.630721
1988	4.530007
1989	5.390975
1990	4.256296
1991	5.080840
1992	4.172421
1993	4.248910
1995	4.536605
1996	4.583184
1997	4.537123
2000	4.164101
2002	4.563031
2003	4.075656
2004	4.447377
2005	4.074093
2006	4.826786
2007	4.911552
2008	4.308592
2009	4.662025
2010	4.239998
2011	4.685099
2012	4.345864
2013	5.170815
2014	4.247590
2015	4.993758
2016	4.315622
2017	5.031076
2018	4.300387
2019	4.284824
2020	3.915817
2022	4.882328

ggplot(winter_standard_dev_all_467_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 467 average winter temperatures for water years 1986-2021

winter MK & SS 467 (corrected)

winter_sd_mk_467_ad <- mk.test(winter_standard_dev_all_467_ad$sd_2)
print(winter_sd_mk_467_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_467_ad$sd_2
## z = -0.20396, n = 31, p-value = 0.8384
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -13.00000000 3461.66666667   -0.02795699

winter_sd_sens_467_ad <- sens.slope(winter_standard_dev_all_467_ad$sd_2)
print(winter_sd_sens_467_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_467_ad$sd_2
## z = -0.20396, n = 31, p-value = 0.8384
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01593830  0.01307104
## sample estimates:
##  Sen's slope 
## -0.001664032

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_467 <- standard_dev_467 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_467 <- spring_standard_dev_all_467 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_467 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.326741
1988	4.912868
1989	5.008660
1990	3.831994
1991	4.690650
1992	4.023824
1993	3.367622
1995	2.924851
1996	4.099916
1997	4.302148
2000	4.674244
2002	3.838982
2003	4.583058
2004	4.140414
2005	3.741618
2006	3.784800
2007	3.960795
2008	3.770284
2009	3.510560
2010	4.008282
2011	3.404504
2012	4.003113
2013	4.528477
2014	4.354371
2015	3.294313
2016	3.368663
2017	4.330573
2018	3.384159
2019	3.616551
2020	4.280672
2022	4.387805

ggplot(spring_standard_dev_all_467, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 467 average spring temperatures for water years 2005-2021

spring MK & SS for 467 (non-corrected)

spring_sd_mk_467 <- mk.test(spring_standard_dev_all_467$sd_2)
print(spring_sd_mk_467)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_467$sd_2
## z = -1.5297, n = 31, p-value = 0.1261
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -91.0000000 3461.6666667   -0.1956989

spring_sd_sens_467 <- sens.slope(spring_standard_dev_all_467$sd_2)
print(spring_sd_sens_467)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_467$sd_2
## z = -1.5297, n = 31, p-value = 0.1261
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.040433402  0.008099548
## sample estimates:
## Sen's slope 
## -0.01778742

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_467 <- standard_dev_467 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_467 <- fall_standard_dev_all_467 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_467 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.150535
1988	3.777988
1989	3.346905
1990	4.172506
1991	4.077039
1992	5.030504
1993	4.027397
1995	4.384327
1996	4.347619
1997	4.343609
2000	4.320396
2002	3.913824
2003	2.984170
2004	4.434295
2005	2.643661
2006	3.818195
2007	3.305078
2008	3.890880
2009	3.644241
2010	4.583592
2011	3.236597
2012	3.182552
2013	3.530531
2014	3.978222
2015	3.535302
2016	3.168156
2017	4.395181
2018	3.929899
2019	3.824415
2020	5.970935
2022	3.680200

ggplot(fall_standard_dev_all_467, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 467 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 467 (non-corrected)

fall_sd_mk_467 <- mk.test(fall_standard_dev_all_467$sd_2)
print(fall_sd_mk_467)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_467$sd_2
## z = -0.37392, n = 31, p-value = 0.7085
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -23.00000000 3461.66666667   -0.04946237

fall_sd_sens_467 <- sens.slope(fall_standard_dev_all_467$sd_2)
print(fall_sd_sens_467)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_467$sd_2
## z = -0.37392, n = 31, p-value = 0.7085
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02977176  0.02406714
## sample estimates:
## Sen's slope 
## -0.00612817

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_467_ad <- standard_dev_467_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_467_ad <- spring_standard_dev_all_467_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_467_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.963305
1988	4.496709
1989	4.589202
1990	3.541552
1991	4.306041
1992	3.691823
1993	3.043919
1995	2.739123
1996	3.763468
1997	3.985882
2000	4.262281
2002	3.500632
2003	4.174684
2004	3.804169
2005	3.427167
2006	3.448435
2007	3.952989
2008	3.804973
2009	3.535751
2010	4.006228
2011	3.390196
2012	3.968383
2013	4.563844
2014	4.366818
2015	3.234748
2016	3.352451
2017	4.307196
2018	3.408838
2019	3.567042
2020	4.291095
2022	4.375108

ggplot(spring_standard_dev_all_467_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 467 average spring temperatures for water years 1986-2021

spring MK & SS 467 (corrected)

spring_sd_mk_467_ad <- mk.test(spring_standard_dev_all_467_ad$sd_2)
print(spring_sd_mk_467_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_467_ad$sd_2
## z = -0.033993, n = 31, p-value = 0.9729
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
## -3.000000e+00  3.461667e+03 -6.451613e-03

spring_sd_sens_467_ad <- sens.slope(spring_standard_dev_all_467_ad$sd_2)
print(spring_sd_sens_467_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_467_ad$sd_2
## z = -0.033993, n = 31, p-value = 0.9729
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02292232  0.02388160
## sample estimates:
##  Sen's slope 
## -0.000597849

Fall

fall_standard_dev_all_467_ad <- standard_dev_467_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_467_ad <- fall_standard_dev_all_467_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_467_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.888808
1988	3.469428
1989	3.123380
1990	3.756769
1991	3.746942
1992	4.658871
1993	3.737681
1995	4.011672
1996	4.005513
1997	3.968226
2000	3.969460
2002	3.600482
2003	2.717745
2004	4.104857
2005	2.384230
2006	3.820552
2007	3.343170
2008	3.819057
2009	3.637540
2010	4.626378
2011	3.220716
2012	3.197842
2013	3.562917
2014	3.993028
2015	3.483963
2016	3.114236
2017	4.358122
2018	3.957780
2019	3.859870
2020	6.044747
2022	3.716374

ggplot(fall_standard_dev_all_467_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 467 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 467 (corrected)

fall_sd_mk_467_ad <- mk.test(fall_standard_dev_all_467_ad$sd_2)
print(fall_sd_mk_467_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_467_ad$sd_2
## z = 0.61187, n = 31, p-value = 0.5406
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 3.700000e+01 3.461667e+03 7.956989e-02

fall_sd_sens_467_ad <- sens.slope(fall_standard_dev_all_467_ad$sd_2)
print(fall_sd_sens_467_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_467_ad$sd_2
## z = 0.61187, n = 31, p-value = 0.5406
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01314265  0.03554773
## sample estimates:
## Sen's slope 
## 0.006691773

Lynx Pass 607

Morrisey 5/22/2006

snotel_607 <- SNOTEL_yampa_area %>% 
  filter(site_id == "607")

#str(snotel_607) # check the date, usually a character.  

snotel_607$Date <- as.Date(snotel_607$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_607_clean <- snotel_607 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_607_clean <- snotel_607_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_607_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_607_clean <- snotel_607_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -40) %>% 
  filter(temperature_mean < 40)

ggplot(snotel_607_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_607_cull_count <- snotel_607_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_607_cull_count

# filtering for too few observations in a year
snotel_607_cull_count_days <- snotel_607_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_607_cull_count_days

## # A tibble: 4 x 2
## # Groups:   waterYear [4]
##   waterYear     n
##       <dbl> <int>
## 1      1985     1
## 2      1994   333
## 3      2019   284
## 4      2020   328

snotel_607_clean_culled <- snotel_607_clean %>% 
  filter(waterYear != "1985" & waterYear != "1986" & waterYear != "1994" & waterYear != "2019" & waterYear != "2020")# & waterYear != "2001" & waterYear != "2021")# & waterYear != "2021")# & waterYear != "1987" & waterYear != "1994" & waterYear != "2002")# & waterYear != "2002" & waterYear != "2016" & waterYear != "2022")# & waterYear != "2017") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_607_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Also 1986

ggplot(snotel_607_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_607_xts <- xts(snotel_607_clean_culled$temperature_mean, order.by = snotel_607_clean_culled$Date)

dygraph(temp_607_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

#snotel_607_clean_culled <- snotel_607_clean_culled %>% 
#  filter(temperature_mean > -30)

#temp_607_xts <- xts(snotel_607_clean_culled$temperature_mean, order.by = snotel_607_clean_culled$Date)

#dygraph(temp_607_xts) %>%
#  dyAxis("y", label = "Daily mean temperature (°C)") 

Lynx Pass 607 Morrisey 5/22/2006

snotel_607_adjusted <- snotel_607_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2006-05-22", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

607 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_607 <- snotel_607_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_607 <- yearly_wy_aver_607 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_607 <- daily_wy_aver_607 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_607$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_607 <-daily_wy_aver_607 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_607$date_temp <- signif(daily_wy_aver2_607$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_607, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

607 SD

standard_dev_607 <- daily_wy_aver_607 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

standard_dev_all_607 <- standard_dev_607 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_607 <- standard_dev_all_607 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_607 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.582343
1988	3.799577
1989	4.524159
1990	3.737210
1991	3.813672
1992	3.699350
1993	3.632591
1995	3.859395
1996	3.710483
1997	3.771008
1998	3.503283
1999	3.824894
2000	3.533504
2001	3.582864
2002	3.816826
2003	3.536193
2004	3.679508
2005	3.506615
2006	3.760379
2007	3.746644
2008	3.417203
2009	3.577805
2010	3.497146
2011	3.661059
2012	3.323317
2013	3.932274
2014	3.438441
2015	3.523553
2016	3.350197
2017	4.100477
2018	3.393477
2021	3.322497
2022	3.810463

ggplot(standard_dev_all_607, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 607 average temperatures for water years 2005-2021

MK & SS for 607 (non-corrected)

sd_mk_607 <- mk.test(standard_dev_all_607$sd_2)
print(sd_mk_607)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_607$sd_2
## z = -2.5256, n = 33, p-value = 0.01155
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -164.0000000 4165.3333333   -0.3106061

sd_sens_607 <- sens.slope(standard_dev_all_607$sd_2)
print(sd_sens_607)

## 
##  Sen's slope
## 
## data:  standard_dev_all_607$sd_2
## z = -2.5256, n = 33, p-value = 0.01155
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.016751375 -0.002635498
## sample estimates:
## Sen's slope 
## -0.01041114

Corrected

607 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_607_ad <- snotel_607_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_607_ad <- yearly_wy_aver_607_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_607_ad <- daily_wy_aver_607_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_607_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_607_ad <-daily_wy_aver_607_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_607_ad$date_temp_ad <- signif(daily_wy_aver2_607_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_607_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

607 SS (corrected)

standard_dev_607_ad <- daily_wy_aver_607_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_607_ad <- standard_dev_607_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_607_ad <- standard_dev_all_607_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_607_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.409194
1988	3.565077
1989	4.368137
1990	3.559308
1991	3.665474
1992	3.525757
1993	3.473881
1995	3.689839
1996	3.530975
1997	3.600786
1998	3.287624
1999	3.679122
2000	3.342181
2001	3.340673
2002	3.548341
2003	3.327490
2004	3.504638
2005	3.361239
2006	3.607575
2007	3.776306
2008	3.433821
2009	3.506260
2010	3.536819
2011	3.653620
2012	3.347204
2013	3.985295
2014	3.414744
2015	3.445791
2016	3.336533
2017	4.044468
2018	3.362640
2021	3.365751
2022	3.812047

ggplot(standard_dev_all_607_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 607 average temperatures for water years 1986-2021

MK & SS 607 (corrected)

sd_mk_607_ad <- mk.test(standard_dev_all_607_ad$sd_2)
print(sd_mk_607_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_607_ad$sd_2
## z = -0.48033, n = 33, p-value = 0.631
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -32.00000000 4165.33333333   -0.06060606

sd_sens_607_ad <- sens.slope(standard_dev_all_607_ad$sd_2)
print(sd_sens_607_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_607_ad$sd_2
## z = -0.48033, n = 33, p-value = 0.631
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.009259148  0.005363338
## sample estimates:
##  Sen's slope 
## -0.002065127

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_607 <- standard_dev_607 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_607 <- summer_standard_dev_all_607 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_607 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.509021
1988	2.222165
1989	2.992402
1990	2.553451
1991	1.992289
1992	2.688367
1993	3.127050
1995	3.088004
1996	1.549095
1997	2.064332
1998	2.812535
1999	1.920085
2000	2.192247
2001	2.568610
2002	2.355194
2003	2.462296
2004	2.556924
2005	2.623972
2006	2.183401
2007	1.937866
2008	2.221198
2009	1.863362
2010	2.187224
2011	1.759141
2012	1.987729
2013	1.994614
2014	1.835703
2015	2.154568
2016	1.892683
2017	1.915960
2018	1.870595
2021	2.426265
2022	2.109108

ggplot(summer_standard_dev_all_607, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 607 average summer temperatures for water years 2005-2021

summer MK & SS for 607 (non-corrected)

summer_sd_mk_607 <- mk.test(summer_standard_dev_all_607$sd_2)
print(summer_sd_mk_607)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_607$sd_2
## z = -2.9284, n = 33, p-value = 0.003407
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -190.0000000 4165.3333333   -0.3598485

summer_sd_sens_607 <- sens.slope(summer_standard_dev_all_607$sd_2)
print(summer_sd_sens_607)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_607$sd_2
## z = -2.9284, n = 33, p-value = 0.003407
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.037019252 -0.005625506
## sample estimates:
## Sen's slope 
## -0.02088598

Winter

winter_standard_dev_all_607 <- standard_dev_607 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_607 <- winter_standard_dev_all_607 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_607 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.305720
1988	4.460102
1989	5.690744
1990	4.537709
1991	4.697436
1992	3.796748
1993	4.306489
1995	4.712720
1996	4.514851
1997	4.508226
1998	4.093395
1999	4.609710
2000	3.982718
2001	4.090879
2002	4.449529
2003	4.212724
2004	4.253297
2005	4.410438
2006	4.726295
2007	4.809553
2008	4.164532
2009	4.295361
2010	4.110187
2011	4.787863
2012	4.030478
2013	4.982548
2014	3.965712
2015	4.385388
2016	4.275599
2017	5.062802
2018	4.230722
2021	3.862622
2022	4.712839

ggplot(winter_standard_dev_all_607, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 607 average winter temperatures for water years 2005-2021

winter MK & SS for 607 (non-corrected)

winter_sd_mk_607 <- mk.test(winter_standard_dev_all_607$sd_2)
print(winter_sd_mk_607)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_607$sd_2
## z = -0.60428, n = 33, p-value = 0.5457
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -40.00000000 4165.33333333   -0.07575758

winter_sd_sens_607 <- sens.slope(winter_standard_dev_all_607$sd_2)
print(winter_sd_sens_607)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_607$sd_2
## z = -0.60428, n = 33, p-value = 0.5457
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.0186793  0.0125724
## sample estimates:
##  Sen's slope 
## -0.005126594

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_607_ad <- standard_dev_607_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_607_ad <- summer_standard_dev_all_607_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_607_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.262800
1988	2.000834
1989	2.676497
1990	2.300297
1991	1.794623
1992	2.422068
1993	2.828743
1995	2.783389
1996	1.392328
1997	1.863039
1998	2.515236
1999	1.713498
2000	1.977694
2001	2.308312
2002	2.109570
2003	2.181472
2004	2.303007
2005	2.333733
2006	2.170289
2007	1.958379
2008	2.237602
2009	1.876691
2010	2.176847
2011	1.747394
2012	1.965829
2013	1.971267
2014	1.837678
2015	2.120516
2016	1.868333
2017	1.892313
2018	1.863227
2021	2.403571
2022	2.095329

ggplot(summer_standard_dev_all_607_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 607 average summer temperatures for water years 1986-2021

summer MK & SS 607 (corrected)

summer_sd_mk_607_ad <- mk.test(summer_standard_dev_all_607_ad$sd_2)
print(summer_sd_mk_607_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_607_ad$sd_2
## z = -1.7509, n = 33, p-value = 0.07997
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -114.0000000 4165.3333333   -0.2159091

summer_sd_sens_607_ad <- sens.slope(summer_standard_dev_all_607_ad$sd_2)
print(summer_sd_sens_607_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_607_ad$sd_2
## z = -1.7509, n = 33, p-value = 0.07997
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.023533697  0.001463671
## sample estimates:
## Sen's slope 
## -0.01124441

Winter

winter_standard_dev_all_607_ad <- standard_dev_607_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_607_ad <- winter_standard_dev_all_607_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_607_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.177345
1988	4.344783
1989	5.652759
1990	4.443225
1991	4.649356
1992	3.697415
1993	4.197014
1995	4.563932
1996	4.382884
1997	4.377624
1998	3.966891
1999	4.481500
2000	3.844152
2001	3.990893
2002	4.318338
2003	4.079920
2004	4.108444
2005	4.300802
2006	4.590842
2007	4.820500
2008	4.167629
2009	4.287540
2010	4.114648
2011	4.782795
2012	4.031624
2013	4.985186
2014	3.958921
2015	4.380114
2016	4.267320
2017	5.077411
2018	4.223291
2021	3.854595
2022	4.714411

ggplot(winter_standard_dev_all_607_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 607 average winter temperatures for water years 1986-2021

winter MK & SS 607 (corrected)

winter_sd_mk_607_ad <- mk.test(winter_standard_dev_all_607_ad$sd_2)
print(winter_sd_mk_607_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_607_ad$sd_2
## z = -0.015494, n = 33, p-value = 0.9876
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
## -2.000000e+00  4.165333e+03 -3.787879e-03

winter_sd_sens_607_ad <- sens.slope(winter_standard_dev_all_607_ad$sd_2)
print(winter_sd_sens_607_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_607_ad$sd_2
## z = -0.015494, n = 33, p-value = 0.9876
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01358995  0.01697849
## sample estimates:
##   Sen's slope 
## -0.0003158058

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_607 <- standard_dev_607 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_607 <- spring_standard_dev_all_607 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_607 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.536935
1988	3.741158
1989	4.208508
1990	3.264941
1991	4.002397
1992	3.110778
1993	2.706393
1995	2.615104
1996	3.649116
1997	3.742304
1998	2.647594
1999	3.944615
2000	4.137037
2001	3.191799
2002	3.027891
2003	3.770674
2004	3.427380
2005	2.955982
2006	2.701304
2007	3.344855
2008	3.270017
2009	3.241549
2010	3.487281
2011	3.087082
2012	3.330254
2013	3.865477
2014	3.878616
2015	2.716340
2016	2.914506
2017	3.971535
2018	2.766661
2021	3.099893
2022	3.984099

ggplot(spring_standard_dev_all_607, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 607 average spring temperatures for water years 2005-2021

spring MK & SS for 607 (non-corrected)

spring_sd_mk_607 <- mk.test(spring_standard_dev_all_607$sd_2)
print(spring_sd_mk_607)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_607$sd_2
## z = -0.48033, n = 33, p-value = 0.631
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -32.00000000 4165.33333333   -0.06060606

spring_sd_sens_607 <- sens.slope(spring_standard_dev_all_607$sd_2)
print(spring_sd_sens_607)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_607$sd_2
## z = -0.48033, n = 33, p-value = 0.631
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.0284678  0.0127500
## sample estimates:
##  Sen's slope 
## -0.006997144

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_607 <- standard_dev_607 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_607 <- fall_standard_dev_all_607 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_607 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.762905
1988	3.258769
1989	2.840806
1990	3.499392
1991	3.217332
1992	4.164700
1993	3.139776
1995	3.035229
1996	3.646304
1997	3.716753
1998	3.578994
1999	3.052388
2000	3.173598
2001	2.856232
2002	2.930051
2003	2.292158
2004	3.431995
2005	2.515351
2006	2.855254
2007	2.953376
2008	2.794251
2009	3.181423
2010	3.490638
2011	2.600636
2012	2.648559
2013	2.967596
2014	3.304237
2015	2.717718
2016	2.491811
2017	3.392230
2018	3.039880
2021	3.046626
2022	2.910269

ggplot(fall_standard_dev_all_607, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 607 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 607 (non-corrected)

fall_sd_mk_607 <- mk.test(fall_standard_dev_all_607$sd_2)
print(fall_sd_mk_607)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_607$sd_2
## z = -1.6269, n = 33, p-value = 0.1038
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -106.0000000 4165.3333333   -0.2007576

fall_sd_sens_607 <- sens.slope(fall_standard_dev_all_607$sd_2)
print(fall_sd_sens_607)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_607$sd_2
## z = -1.6269, n = 33, p-value = 0.1038
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.028149221  0.002844073
## sample estimates:
## Sen's slope 
## -0.01329466

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_607_ad <- standard_dev_607_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_607_ad <- spring_standard_dev_all_607_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_607_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.260283
1988	3.437487
1989	3.878689
1990	3.032910
1991	3.688092
1992	2.867862
1993	2.485990
1995	2.449444
1996	3.358340
1997	3.484411
1998	2.393530
1999	3.649176
2000	3.775712
2001	2.929607
2002	2.785401
2003	3.441423
2004	3.147513
2005	2.700594
2006	2.499929
2007	3.330419
2008	3.316341
2009	3.279967
2010	3.503983
2011	3.066010
2012	3.282069
2013	3.901010
2014	3.894027
2015	2.650359
2016	2.888094
2017	3.928364
2018	2.796806
2021	3.104692
2022	3.973703

ggplot(spring_standard_dev_all_607_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 607 average spring temperatures for water years 1986-2021

spring MK & SS 607 (corrected)

spring_sd_mk_607_ad <- mk.test(spring_standard_dev_all_607_ad$sd_2)
print(spring_sd_mk_607_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_607_ad$sd_2
## z = 0.60428, n = 33, p-value = 0.5457
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 4.000000e+01 4.165333e+03 7.575758e-02

spring_sd_sens_607_ad <- sens.slope(spring_standard_dev_all_607_ad$sd_2)
print(spring_sd_sens_607_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_607_ad$sd_2
## z = 0.60428, n = 33, p-value = 0.5457
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01703698  0.02474808
## sample estimates:
## Sen's slope 
## 0.006352082

Fall

fall_standard_dev_all_607_ad <- standard_dev_607_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_607_ad <- fall_standard_dev_all_607_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_607_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.558069
1988	3.011138
1989	2.626619
1990	3.160763
1991	2.967966
1992	3.872921
1993	2.933684
1995	2.752599
1996	3.368412
1997	3.410403
1998	3.224511
1999	2.851718
2000	2.891918
2001	2.614152
2002	2.714288
2003	2.103480
2004	3.194405
2005	2.316253
2006	2.922116
2007	3.031155
2008	2.740938
2009	3.181195
2010	3.529566
2011	2.599997
2012	2.686942
2013	3.005285
2014	3.332121
2015	2.653992
2016	2.442224
2017	3.348174
2018	3.077504
2021	3.027465
2022	2.960297

ggplot(fall_standard_dev_all_607_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 607 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 607 (corrected)

fall_sd_mk_607_ad <- mk.test(fall_standard_dev_all_607_ad$sd_2)
print(fall_sd_mk_607_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_607_ad$sd_2
## z = -0.077472, n = 33, p-value = 0.9382
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##   -6.00000000 4165.33333333   -0.01136364

fall_sd_sens_607_ad <- sens.slope(fall_standard_dev_all_607_ad$sd_2)
print(fall_sd_sens_607_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_607_ad$sd_2
## z = -0.077472, n = 33, p-value = 0.9382
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01477973  0.01283930
## sample estimates:
##   Sen's slope 
## -0.0006022318

Rabbit Ears 709

Morrisey 8/7/2006

snotel_709 <- SNOTEL_yampa_area %>% 
  filter(site_id == "709")

#str(snotel_709) # check the date, usually a character.  

snotel_709$Date <- as.Date(snotel_709$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_709_clean <- snotel_709 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_709_clean <- snotel_709_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_709_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_709_clean <- snotel_709_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -40) %>% 
  filter(temperature_mean < 40)

ggplot(snotel_709_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_709_cull_count <- snotel_709_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_709_cull_count

# filtering for too few observations in a year
snotel_709_cull_count_days <- snotel_709_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_709_cull_count_days

## # A tibble: 14 x 2
## # Groups:   waterYear [14]
##    waterYear     n
##        <dbl> <int>
##  1      1992   318
##  2      1993   293
##  3      1994   332
##  4      1995   169
##  5      2006   348
##  6      2007   311
##  7      2011   292
##  8      2012   308
##  9      2013   300
## 10      2014   283
## 11      2015    44
## 12      2016    18
## 13      2017    34
## 14      2018   147

snotel_709_clean_culled <- snotel_709_clean %>% 
  filter(waterYear > "1995" & waterYear != "2006" & waterYear != "2007" & waterYear != "2011" & waterYear != "2012" & waterYear != "2013" & waterYear != "2014" & waterYear != "2015" & waterYear != "2016" & waterYear != "2017" & waterYear != "2018")# & waterYear != "2002")# & waterYear != "2002" & waterYear != "2016" & waterYear != "2022")# & waterYear != "2017") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_709_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

ggplot(snotel_709_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_709_xts <- xts(snotel_709_clean_culled$temperature_mean, order.by = snotel_709_clean_culled$Date)

dygraph(temp_709_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

#snotel_709_clean_culled <- snotel_709_clean_culled %>% 
#  filter(temperature_mean > -30)

#temp_709_xts <- xts(snotel_709_clean_culled$temperature_mean, order.by = snotel_709_clean_culled$Date)

#dygraph(temp_709_xts) %>%
#  dyAxis("y", label = "Daily mean temperature (°C)") 

Rabbit Ears 709 Morrisey 8/7/2006

snotel_709_adjusted <- snotel_709_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2006-08-07", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

709 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_709 <- snotel_709_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_709 <- yearly_wy_aver_709 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_709 <- daily_wy_aver_709 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_709$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_709 <-daily_wy_aver_709 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_709$date_temp <- signif(daily_wy_aver2_709$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_709, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

709 SD

standard_dev_709 <- daily_wy_aver_709 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

standard_dev_all_709 <- standard_dev_709 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_709 <- standard_dev_all_709 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_709 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1996	4.046429
1997	4.039956
1998	3.603214
1999	4.110191
2000	3.917364
2001	3.864370
2002	3.983878
2003	3.694470
2004	4.063015
2005	3.645949
2008	3.750942
2009	3.755342
2010	3.897555
2019	3.594822
2020	4.019790
2021	3.795834
2022	4.013440

ggplot(standard_dev_all_709, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 709 average temperatures for water years 2005-2021

MK & SS for 709 (non-corrected)

sd_mk_709 <- mk.test(standard_dev_all_709$sd_2)
print(sd_mk_709)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_709$sd_2
## z = -0.86505, n = 17, p-value = 0.387
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##           S        varS         tau 
## -22.0000000 589.3333333  -0.1617647

sd_sens_709 <- sens.slope(standard_dev_all_709$sd_2)
print(sd_sens_709)

## 
##  Sen's slope
## 
## data:  standard_dev_all_709$sd_2
## z = -0.86505, n = 17, p-value = 0.387
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.03211267  0.01481691
## sample estimates:
##  Sen's slope 
## -0.007323263

Corrected

709 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_709_ad <- snotel_709_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_709_ad <- yearly_wy_aver_709_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_709_ad <- daily_wy_aver_709_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_709_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_709_ad <-daily_wy_aver_709_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_709_ad$date_temp_ad <- signif(daily_wy_aver2_709_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_709_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

709 SS (corrected)

standard_dev_709_ad <- daily_wy_aver_709_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_709_ad <- standard_dev_709_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_709_ad <- standard_dev_all_709_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_709_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1996	3.846082
1997	3.846388
1998	3.374129
1999	3.941368
2000	3.683076
2001	3.602903
2002	3.708201
2003	3.456346
2004	3.852331
2005	3.467358
2008	3.776391
2009	3.691358
2010	3.912619
2019	3.608731
2020	4.047964
2021	3.821569
2022	3.998666

ggplot(standard_dev_all_709_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 709 average temperatures for water years 1986-2021

MK & SS 709 (corrected)

sd_mk_709_ad <- mk.test(standard_dev_all_709_ad$sd_2)
print(sd_mk_709_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_709_ad$sd_2
## z = 1.1946, n = 17, p-value = 0.2322
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##           S        varS         tau 
##  30.0000000 589.3333333   0.2205882

sd_sens_709_ad <- sens.slope(standard_dev_all_709_ad$sd_2)
print(sd_sens_709_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_709_ad$sd_2
## z = 1.1946, n = 17, p-value = 0.2322
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01406580  0.03534324
## sample estimates:
## Sen's slope 
##  0.01259339

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_709 <- standard_dev_709 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_709 <- summer_standard_dev_all_709 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_709 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1996	1.798172
1997	2.581032
1998	2.950365
1999	2.075320
2000	2.584201
2001	3.028438
2002	2.885638
2003	2.760048
2004	2.958099
2005	3.021450
2008	2.580371
2009	2.282856
2010	2.413484
2019	2.541279
2020	2.793659
2021	3.288074
2022	2.423721

ggplot(summer_standard_dev_all_709, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 709 average summer temperatures for water years 2005-2021

summer MK & SS for 709 (non-corrected)

summer_sd_mk_709 <- mk.test(summer_standard_dev_all_709$sd_2)
print(summer_sd_mk_709)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_709$sd_2
## z = 0.45312, n = 17, p-value = 0.6505
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  12.00000000 589.33333333   0.08823529

summer_sd_sens_709 <- sens.slope(summer_standard_dev_all_709$sd_2)
print(summer_sd_sens_709)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_709$sd_2
## z = 0.45312, n = 17, p-value = 0.6505
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.03646145  0.06092116
## sample estimates:
## Sen's slope 
##  0.01865082

Winter

winter_standard_dev_all_709 <- standard_dev_709 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_709 <- winter_standard_dev_all_709 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_709 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1996	4.501936
1997	4.613454
1998	3.995501
1999	4.729453
2000	4.078328
2001	4.144973
2002	4.375561
2003	3.993018
2004	4.319516
2005	4.156150
2008	4.301765
2009	4.435250
2010	4.226483
2019	3.994256
2020	3.779755
2021	3.934384
2022	4.695839

ggplot(winter_standard_dev_all_709, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 709 average winter temperatures for water years 2005-2021

winter MK & SS for 709 (non-corrected)

winter_sd_mk_709 <- mk.test(winter_standard_dev_all_709$sd_2)
print(winter_sd_mk_709)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_709$sd_2
## z = -1.1946, n = 17, p-value = 0.2322
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##           S        varS         tau 
## -30.0000000 589.3333333  -0.2205882

winter_sd_sens_709 <- sens.slope(winter_standard_dev_all_709$sd_2)
print(winter_sd_sens_709)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_709$sd_2
## z = -1.1946, n = 17, p-value = 0.2322
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.05158440  0.02309819
## sample estimates:
## Sen's slope 
## -0.02106068

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_709_ad <- standard_dev_709_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_709_ad <- summer_standard_dev_all_709_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_709_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1996	1.622328
1997	2.341696
1998	2.632811
1999	1.873769
2000	2.338610
2001	2.744766
2002	2.617040
2003	2.432490
2004	2.678525
2005	2.690760
2008	2.599563
2009	2.296096
2010	2.397384
2019	2.559431
2020	2.755521
2021	3.214722
2022	2.387394

ggplot(summer_standard_dev_all_709_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 709 average summer temperatures for water years 1986-2021

summer MK & SS 709 (corrected)

summer_sd_mk_709_ad <- mk.test(summer_standard_dev_all_709_ad$sd_2)
print(summer_sd_mk_709_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_709_ad$sd_2
## z = 1.5241, n = 17, p-value = 0.1275
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##           S        varS         tau 
##  38.0000000 589.3333333   0.2794118

summer_sd_sens_709_ad <- sens.slope(summer_standard_dev_all_709_ad$sd_2)
print(summer_sd_sens_709_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_709_ad$sd_2
## z = 1.5241, n = 17, p-value = 0.1275
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.004559968  0.072084836
## sample estimates:
## Sen's slope 
##   0.0296972

Winter

winter_standard_dev_all_709_ad <- standard_dev_709_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_709_ad <- winter_standard_dev_all_709_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_709_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1996	4.357677
1997	4.463267
1998	3.865908
1999	4.568776
2000	3.890382
2001	4.031648
2002	4.229187
2003	3.858395
2004	4.163530
2005	4.026833
2008	4.310811
2009	4.427496
2010	4.229217
2019	3.977640
2020	3.780200
2021	3.922802
2022	4.693983

ggplot(winter_standard_dev_all_709_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 709 average winter temperatures for water years 1986-2021

winter MK & SS 709 (corrected)

winter_sd_mk_709_ad <- mk.test(winter_standard_dev_all_709_ad$sd_2)
print(winter_sd_mk_709_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_709_ad$sd_2
## z = -0.37073, n = 17, p-value = 0.7108
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -10.00000000 589.33333333  -0.07352941

winter_sd_sens_709_ad <- sens.slope(winter_standard_dev_all_709_ad$sd_2)
print(winter_sd_sens_709_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_709_ad$sd_2
## z = -0.37073, n = 17, p-value = 0.7108
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.03772869  0.04235444
## sample estimates:
##  Sen's slope 
## -0.006946645

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_709 <- standard_dev_709 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_709 <- spring_standard_dev_all_709 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_709 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1996	4.392525
1997	3.979770
1998	3.287391
1999	4.396265
2000	4.698179
2001	3.870953
2002	3.612179
2003	4.491124
2004	4.167010
2005	3.897487
2008	3.728142
2009	3.468541
2010	4.289775
2019	3.872565
2020	3.990448
2021	3.789377
2022	4.306624

ggplot(spring_standard_dev_all_709, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 709 average spring temperatures for water years 2005-2021

spring MK & SS for 709 (non-corrected)

spring_sd_mk_709 <- mk.test(spring_standard_dev_all_709$sd_2)
print(spring_sd_mk_709)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_709$sd_2
## z = -0.45312, n = 17, p-value = 0.6505
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -12.00000000 589.33333333  -0.08823529

spring_sd_sens_709 <- sens.slope(spring_standard_dev_all_709$sd_2)
print(spring_sd_sens_709)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_709$sd_2
## z = -0.45312, n = 17, p-value = 0.6505
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.05500423  0.03719803
## sample estimates:
##  Sen's slope 
## -0.009609552

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_709 <- standard_dev_709 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_709 <- fall_standard_dev_all_709 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_709 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1996	4.724749
1997	4.272893
1998	3.639717
1999	3.877520
2000	4.287897
2001	3.487207
2002	3.745845
2003	2.892469
2004	4.324309
2005	2.740906
2008	3.758002
2009	3.389929
2010	4.415185
2019	3.613747
2020	5.551894
2021	4.097061
2022	3.580181

ggplot(fall_standard_dev_all_709, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 709 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 709 (non-corrected)

fall_sd_mk_709 <- mk.test(fall_standard_dev_all_709$sd_2)
print(fall_sd_mk_709)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_709$sd_2
## z = -0.45312, n = 17, p-value = 0.6505
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -12.00000000 589.33333333  -0.08823529

fall_sd_sens_709 <- sens.slope(fall_standard_dev_all_709$sd_2)
print(fall_sd_sens_709)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_709$sd_2
## z = -0.45312, n = 17, p-value = 0.6505
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.08829641  0.06098540
## sample estimates:
## Sen's slope 
## -0.01682022

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_709_ad <- standard_dev_709_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_709_ad <- spring_standard_dev_all_709_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_709_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1996	4.076432
1997	3.718638
1998	2.996424
1999	4.095541
2000	4.329527
2001	3.566542
2002	3.333462
2003	4.140158
2004	3.859844
2005	3.607138
2008	3.761801
2009	3.474898
2010	4.287627
2019	3.802435
2020	4.001186
2021	3.784079
2022	4.282196

ggplot(spring_standard_dev_all_709_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 709 average spring temperatures for water years 1986-2021

spring MK & SS 709 (corrected)

spring_sd_mk_709_ad <- mk.test(spring_standard_dev_all_709_ad$sd_2)
print(spring_sd_mk_709_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_709_ad$sd_2
## z = 0.70027, n = 17, p-value = 0.4838
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##           S        varS         tau 
##  18.0000000 589.3333333   0.1323529

spring_sd_sens_709_ad <- sens.slope(spring_standard_dev_all_709_ad$sd_2)
print(spring_sd_sens_709_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_709_ad$sd_2
## z = 0.70027, n = 17, p-value = 0.4838
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02707345  0.06505950
## sample estimates:
## Sen's slope 
##  0.01320254

Fall

fall_standard_dev_all_709_ad <- standard_dev_709_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_709_ad <- fall_standard_dev_all_709_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_709_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1996	4.395293
1997	3.948034
1998	3.280831
1999	3.640720
2000	3.974748
2001	3.196307
2002	3.476675
2003	2.663726
2004	4.028859
2005	2.514890
2008	3.673576
2009	3.379781
2010	4.443400
2019	3.643612
2020	5.616771
2021	4.119851
2022	3.600881

ggplot(fall_standard_dev_all_709_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 709 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 709 (corrected)

fall_sd_mk_709_ad <- mk.test(fall_standard_dev_all_709_ad$sd_2)
print(fall_sd_mk_709_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_709_ad$sd_2
## z = 0.45312, n = 17, p-value = 0.6505
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  12.00000000 589.33333333   0.08823529

fall_sd_sens_709_ad <- sens.slope(fall_standard_dev_all_709_ad$sd_2)
print(fall_sd_sens_709_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_709_ad$sd_2
## z = 0.45312, n = 17, p-value = 0.6505
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.05682529  0.09235443
## sample estimates:
## Sen's slope 
##  0.01190958

Ripple Creek 717

Oyler -> Morrisey 8/7/2006

snotel_717 <- SNOTEL_yampa_area %>% 
  filter(site_id == "717")

#str(snotel_717) # check the date, usually a character.  

snotel_717$Date <- as.Date(snotel_717$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_717_clean <- snotel_717 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_717_clean <- snotel_717_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_717_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_717_clean <- snotel_717_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -40) %>% 
  filter(temperature_mean < 40)

ggplot(snotel_717_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_717_cull_count <- snotel_717_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_717_cull_count

# filtering for too few observations in a year
snotel_717_cull_count_days <- snotel_717_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_717_cull_count_days

## # A tibble: 2 x 2
## # Groups:   waterYear [2]
##   waterYear     n
##       <dbl> <int>
## 1      1992   311
## 2      1993   330

snotel_717_clean_culled <- snotel_717_clean %>% 
  filter(waterYear != "1992" & waterYear != "1993")# & waterYear != "2007" & waterYear != "2011" & waterYear != "2012" & waterYear != "2013" & waterYear != "2014" & waterYear != "2015" & waterYear != "2016" & waterYear != "2017" & waterYear != "2018")# & waterYear != "2002")# & waterYear != "2002" & waterYear != "2016" & waterYear != "2022")# & waterYear != "2017") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_717_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

ggplot(snotel_717_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_717_xts <- xts(snotel_717_clean_culled$temperature_mean, order.by = snotel_717_clean_culled$Date)

dygraph(temp_717_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

#snotel_717_clean_culled <- snotel_717_clean_culled %>% 
#  filter(temperature_mean > -30)

#temp_717_xts <- xts(snotel_717_clean_culled$temperature_mean, order.by = snotel_717_clean_culled$Date)

#dygraph(temp_717_xts) %>%
#  dyAxis("y", label = "Daily mean temperature (°C)") 

Ripple Creek 717 Oyler -> Morrisey 8/7/2006

snotel_717_adjusted <- snotel_717_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2006-08-07", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

717 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_717 <- snotel_717_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_717 <- yearly_wy_aver_717 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_717 <- daily_wy_aver_717 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_717$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_717 <-daily_wy_aver_717 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_717$date_temp <- signif(daily_wy_aver2_717$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_717, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

717 SD

standard_dev_717 <- daily_wy_aver_717 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

standard_dev_all_717 <- standard_dev_717 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_717 <- standard_dev_all_717 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_717 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.992946
1988	4.081187
1989	4.268444
1990	3.883613
1991	3.974438
1994	3.840813
1995	4.082652
1996	3.962314
1997	3.927417
1998	3.701477
1999	3.993733
2000	4.010976
2001	3.808629
2002	3.974543
2003	3.790376
2004	4.027345
2005	3.654554
2006	4.108348
2007	3.948026
2008	3.836531
2009	3.765057
2010	3.804487
2011	3.866990
2012	3.662769
2013	4.076981
2014	3.762042
2015	3.936033
2016	3.526473
2017	4.156233
2018	3.516048
2019	3.526563
2020	3.954049
2021	3.859996
2022	4.067130

ggplot(standard_dev_all_717, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 717 average temperatures for water years 2005-2021

MK & SS for 717 (non-corrected)

sd_mk_717 <- mk.test(standard_dev_all_717$sd_2)
print(sd_mk_717)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_717$sd_2
## z = -1.9568, n = 34, p-value = 0.05037
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -133.0000000 4550.3333333   -0.2370766

sd_sens_717 <- sens.slope(standard_dev_all_717$sd_2)
print(sd_sens_717)

## 
##  Sen's slope
## 
## data:  standard_dev_all_717$sd_2
## z = -1.9568, n = 34, p-value = 0.05037
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -1.417852e-02  1.170191e-05
## sample estimates:
##  Sen's slope 
## -0.006354918

Corrected

717 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_717_ad <- snotel_717_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_717_ad <- yearly_wy_aver_717_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_717_ad <- daily_wy_aver_717_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_717_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_717_ad <-daily_wy_aver_717_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_717_ad$date_temp_ad <- signif(daily_wy_aver2_717_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_717_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

717 SS (corrected)

standard_dev_717_ad <- daily_wy_aver_717_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_717_ad <- standard_dev_717_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_717_ad <- standard_dev_all_717_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_717_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.782725
1988	3.822012
1989	4.062405
1990	3.649173
1991	3.803469
1994	3.610143
1995	3.895253
1996	3.761608
1997	3.737641
1998	3.474078
1999	3.844055
2000	3.789521
2001	3.570768
2002	3.706119
2003	3.546337
2004	3.836887
2005	3.488400
2006	3.954787
2007	3.961826
2008	3.862141
2009	3.715647
2010	3.811776
2011	3.867504
2012	3.665082
2013	4.099951
2014	3.741901
2015	3.858066
2016	3.516673
2017	4.110060
2018	3.494338
2019	3.540473
2020	3.980586
2021	3.885063
2022	4.059626

ggplot(standard_dev_all_717_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 717 average temperatures for water years 1986-2021

MK & SS 717 (corrected)

sd_mk_717_ad <- mk.test(standard_dev_all_717_ad$sd_2)
print(sd_mk_717_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_717_ad$sd_2
## z = 0.88947, n = 34, p-value = 0.3738
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   61.0000000 4550.3333333    0.1087344

sd_sens_717_ad <- sens.slope(standard_dev_all_717_ad$sd_2)
print(sd_sens_717_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_717_ad$sd_2
## z = 0.88947, n = 34, p-value = 0.3738
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.004837281  0.009372664
## sample estimates:
## Sen's slope 
## 0.002527203

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_717 <- standard_dev_717 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_717 <- summer_standard_dev_all_717 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_717 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.143471
1988	2.329515
1989	3.133187
1990	3.173442
1991	2.514904
1994	2.554514
1995	3.707395
1996	1.949616
1997	2.413608
1998	3.297268
1999	2.083035
2000	2.628543
2001	2.921813
2002	2.746366
2003	2.993916
2004	2.886182
2005	3.143443
2006	2.896111
2007	2.450509
2008	2.563005
2009	2.410173
2010	2.308791
2011	2.264653
2012	2.381496
2013	2.189274
2014	2.354949
2015	2.582685
2016	2.278792
2017	2.085138
2018	2.281696
2019	2.619712
2020	2.751195
2021	3.242236
2022	2.424182

ggplot(summer_standard_dev_all_717, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 717 average summer temperatures for water years 2005-2021

summer MK & SS for 717 (non-corrected)

summer_sd_mk_717 <- mk.test(summer_standard_dev_all_717$sd_2)
print(summer_sd_mk_717)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_717$sd_2
## z = -1.7493, n = 34, p-value = 0.08024
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -119.0000000 4550.3333333   -0.2121212

summer_sd_sens_717 <- sens.slope(summer_standard_dev_all_717$sd_2)
print(summer_sd_sens_717)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_717$sd_2
## z = -1.7493, n = 34, p-value = 0.08024
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.031536692  0.001341484
## sample estimates:
## Sen's slope 
## -0.01427771

Winter

winter_standard_dev_all_717 <- standard_dev_717 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_717 <- winter_standard_dev_all_717 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_717 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.499203
1988	4.475411
1989	5.077805
1990	4.217163
1991	4.761805
1994	4.503071
1995	4.619426
1996	4.372782
1997	4.307120
1998	3.968149
1999	4.523894
2000	4.413746
2001	4.134155
2002	4.394665
2003	3.966590
2004	4.427422
2005	4.205895
2006	4.851298
2007	4.783357
2008	4.407971
2009	4.458470
2010	4.115693
2011	4.810093
2012	4.294137
2013	5.036856
2014	4.131160
2015	4.636826
2016	4.267271
2017	4.834320
2018	4.134957
2019	4.038126
2020	3.885231
2021	4.108951
2022	4.744366

ggplot(winter_standard_dev_all_717, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 717 average winter temperatures for water years 2005-2021

winter MK & SS for 717 (non-corrected)

winter_sd_mk_717 <- mk.test(winter_standard_dev_all_717$sd_2)
print(winter_sd_mk_717)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_717$sd_2
## z = -1.3046, n = 34, p-value = 0.192
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -89.0000000 4550.3333333   -0.1586453

winter_sd_sens_717 <- sens.slope(winter_standard_dev_all_717$sd_2)
print(winter_sd_sens_717)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_717$sd_2
## z = -1.3046, n = 34, p-value = 0.192
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.018331767  0.005096296
## sample estimates:
##  Sen's slope 
## -0.008005424

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_717_ad <- standard_dev_717_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_717_ad <- summer_standard_dev_all_717_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_717_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.837065
1988	2.093151
1989	2.798815
1990	2.860679
1991	2.267217
1994	2.310820
1995	3.340008
1996	1.750528
1997	2.176964
1998	2.946304
1999	1.861239
2000	2.373269
2001	2.640689
2002	2.474230
2003	2.649636
2004	2.607153
2005	2.797558
2006	2.701214
2007	2.466229
2008	2.590996
2009	2.445613
2010	2.309029
2011	2.270348
2012	2.339717
2013	2.154672
2014	2.354070
2015	2.549937
2016	2.245147
2017	2.057727
2018	2.260666
2019	2.640724
2020	2.744352
2021	3.200351
2022	2.401328

ggplot(summer_standard_dev_all_717_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 717 average summer temperatures for water years 1986-2021

summer MK & SS 717 (corrected)

summer_sd_mk_717_ad <- mk.test(summer_standard_dev_all_717_ad$sd_2)
print(summer_sd_mk_717_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_717_ad$sd_2
## z = -0.62263, n = 34, p-value = 0.5335
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -43.00000000 4550.33333333   -0.07664884

summer_sd_sens_717_ad <- sens.slope(summer_standard_dev_all_717_ad$sd_2)
print(summer_sd_sens_717_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_717_ad$sd_2
## z = -0.62263, n = 34, p-value = 0.5335
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01918573  0.01114975
## sample estimates:
##  Sen's slope 
## -0.004088186

Winter

winter_standard_dev_all_717_ad <- standard_dev_717_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_717_ad <- winter_standard_dev_all_717_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_717_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.367624
1988	4.363759
1989	4.960980
1990	4.100642
1991	4.672601
1994	4.400390
1995	4.476852
1996	4.247078
1997	4.163653
1998	3.852083
1999	4.384472
2000	4.234482
2001	4.043977
2002	4.267181
2003	3.856679
2004	4.286247
2005	4.098262
2006	4.733071
2007	4.791416
2008	4.418437
2009	4.453741
2010	4.119044
2011	4.809006
2012	4.291916
2013	5.036775
2014	4.128885
2015	4.631930
2016	4.261038
2017	4.845159
2018	4.128668
2019	4.027230
2020	3.888800
2021	4.104457
2022	4.743054

ggplot(winter_standard_dev_all_717_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 717 average winter temperatures for water years 1986-2021

winter MK & SS 717 (corrected)

winter_sd_mk_717_ad <- mk.test(winter_standard_dev_all_717_ad$sd_2)
print(winter_sd_mk_717_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_717_ad$sd_2
## z = -0.23719, n = 34, p-value = 0.8125
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -17.00000000 4550.33333333   -0.03030303

winter_sd_sens_717_ad <- sens.slope(winter_standard_dev_all_717_ad$sd_2)
print(winter_sd_sens_717_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_717_ad$sd_2
## z = -0.23719, n = 34, p-value = 0.8125
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01195014  0.01072681
## sample estimates:
##  Sen's slope 
## -0.002045206

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_717 <- standard_dev_717 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_717 <- spring_standard_dev_all_717 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_717 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.915288
1988	4.552524
1989	4.084735
1990	3.511877
1991	3.993001
1994	3.670914
1995	3.130044
1996	4.302921
1997	4.297618
1998	3.380682
1999	4.437436
2000	4.588449
2001	3.896187
2002	3.726636
2003	4.610864
2004	3.758258
2005	3.676604
2006	3.521178
2007	3.924077
2008	3.829295
2009	3.311054
2010	4.043445
2011	3.273519
2012	3.853739
2013	4.171176
2014	4.332028
2015	3.200452
2016	3.308506
2017	4.181797
2018	3.207366
2019	3.510591
2020	3.944077
2021	3.858749
2022	4.250542

ggplot(spring_standard_dev_all_717, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 717 average spring temperatures for water years 2005-2021

spring MK & SS for 717 (non-corrected)

spring_sd_mk_717 <- mk.test(spring_standard_dev_all_717$sd_2)
print(spring_sd_mk_717)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_717$sd_2
## z = -0.85982, n = 34, p-value = 0.3899
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -59.0000000 4550.3333333   -0.1051693

spring_sd_sens_717 <- sens.slope(spring_standard_dev_all_717$sd_2)
print(spring_sd_sens_717)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_717$sd_2
## z = -0.85982, n = 34, p-value = 0.3899
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.025113649  0.009518157
## sample estimates:
##  Sen's slope 
## -0.008243287

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_717 <- standard_dev_717 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_717 <- fall_standard_dev_all_717 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_717 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.300996
1988	3.692732
1989	3.016863
1990	4.264319
1991	3.608502
1994	3.019284
1995	3.330218
1996	4.462253
1997	4.385067
1998	3.805551
1999	3.642157
2000	4.106109
2001	3.459445
2002	3.723556
2003	3.084738
2004	4.441646
2005	2.676165
2006	3.511499
2007	3.181780
2008	3.827247
2009	3.496022
2010	4.464998
2011	3.244665
2012	3.152114
2013	3.386952
2014	3.827335
2015	3.433937
2016	3.053215
2017	4.159668
2018	3.579810
2019	3.411787
2020	5.258055
2021	4.002369
2022	3.553143

ggplot(fall_standard_dev_all_717, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 717 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 717 (non-corrected)

fall_sd_mk_717 <- mk.test(fall_standard_dev_all_717$sd_2)
print(fall_sd_mk_717)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_717$sd_2
## z = 0.41508, n = 34, p-value = 0.6781
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   29.0000000 4550.3333333    0.0516934

fall_sd_sens_717 <- sens.slope(fall_standard_dev_all_717$sd_2)
print(fall_sd_sens_717)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_717$sd_2
## z = 0.41508, n = 34, p-value = 0.6781
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01594574  0.02084988
## sample estimates:
## Sen's slope 
## 0.003892044

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_717_ad <- standard_dev_717_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_717_ad <- spring_standard_dev_all_717_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_717_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.626498
1988	4.222830
1989	3.775377
1990	3.296075
1991	3.723715
1994	3.376716
1995	2.949087
1996	3.996385
1997	4.023573
1998	3.104451
1999	4.147730
2000	4.236400
2001	3.599100
2002	3.435452
2003	4.249693
2004	3.490958
2005	3.395982
2006	3.250296
2007	3.910671
2008	3.859653
2009	3.332855
2010	4.051319
2011	3.271206
2012	3.826297
2013	4.189788
2014	4.344861
2015	3.144249
2016	3.289767
2017	4.168952
2018	3.238819
2019	3.461501
2020	3.952389
2021	3.845782
2022	4.241782

ggplot(spring_standard_dev_all_717_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 717 average spring temperatures for water years 1986-2021

spring MK & SS 717 (corrected)

spring_sd_mk_717_ad <- mk.test(spring_standard_dev_all_717_ad$sd_2)
print(spring_sd_mk_717_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_717_ad$sd_2
## z = 0.44473, n = 34, p-value = 0.6565
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 3.100000e+01 4.550333e+03 5.525847e-02

spring_sd_sens_717_ad <- sens.slope(spring_standard_dev_all_717_ad$sd_2)
print(spring_sd_sens_717_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_717_ad$sd_2
## z = 0.44473, n = 34, p-value = 0.6565
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01216283  0.01937335
## sample estimates:
## Sen's slope 
## 0.003391378

Fall

fall_standard_dev_all_717_ad <- standard_dev_717_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_717_ad <- fall_standard_dev_all_717_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_717_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.048081
1988	3.417611
1989	2.815361
1990	3.881493
1991	3.361460
1994	2.732692
1995	3.030575
1996	4.143793
1997	4.065907
1998	3.469235
1999	3.416906
2000	3.808552
2001	3.164955
2002	3.453855
2003	2.851065
2004	4.136895
2005	2.456142
2006	3.586155
2007	3.228872
2008	3.768488
2009	3.488571
2010	4.504971
2011	3.228025
2012	3.167645
2013	3.392653
2014	3.851091
2015	3.378543
2016	3.003291
2017	4.112073
2018	3.589000
2019	3.462996
2020	5.308473
2021	4.010569
2022	3.607163

ggplot(fall_standard_dev_all_717_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 717 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 717 (corrected)

fall_sd_mk_717_ad <- mk.test(fall_standard_dev_all_717_ad$sd_2)
print(fall_sd_mk_717_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_717_ad$sd_2
## z = 1.6603, n = 34, p-value = 0.09685
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##           S        varS         tau 
##  113.000000 4550.333333    0.201426

fall_sd_sens_717_ad <- sens.slope(fall_standard_dev_all_717_ad$sd_2)
print(fall_sd_sens_717_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_717_ad$sd_2
## z = 1.6603, n = 34, p-value = 0.09685
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.001732358  0.033074963
## sample estimates:
## Sen's slope 
##   0.0143572

Tower 825

Original 8/18/2004

snotel_825 <- SNOTEL_yampa_area %>% 
  filter(site_id == "825")

#str(snotel_825) # check the date, usually a character.  

snotel_825$Date <- as.Date(snotel_825$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_825_clean <- snotel_825 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_825_clean <- snotel_825_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_825_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_825_clean <- snotel_825_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -40) %>% 
  filter(temperature_mean < 30)

ggplot(snotel_825_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_825_cull_count <- snotel_825_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_825_cull_count

# filtering for too few observations in a year
snotel_825_cull_count_days <- snotel_825_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_825_cull_count_days

## # A tibble: 9 x 2
## # Groups:   waterYear [9]
##   waterYear     n
##       <dbl> <int>
## 1      1985     1
## 2      1987   348
## 3      1994   301
## 4      1995   347
## 5      1997   322
## 6      1998   343
## 7      1999   348
## 8      2002   327
## 9      2008   325

snotel_825_clean_culled <- snotel_825_clean %>% 
  filter(waterYear > "1987" & waterYear != "1994" & waterYear != "1995" & waterYear != "1997" & waterYear != "1998" & waterYear != "1999" & waterYear != "2002" & waterYear != "2008")# & waterYear != "2017" & waterYear != "2018")# & waterYear != "2002")# & waterYear != "2002" & waterYear != "2016" & waterYear != "2022")# & waterYear != "2017") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_825_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

ggplot(snotel_825_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_825_xts <- xts(snotel_825_clean_culled$temperature_mean, order.by = snotel_825_clean_culled$Date)

dygraph(temp_825_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

#snotel_825_clean_culled <- snotel_825_clean_culled %>% 
#  filter(temperature_mean > -30)

#temp_825_xts <- xts(snotel_825_clean_culled$temperature_mean, order.by = snotel_825_clean_culled$Date)

#dygraph(temp_825_xts) %>%
#  dyAxis("y", label = "Daily mean temperature (°C)") 

Tower 825 Original 8/18/2004

snotel_825_adjusted <- snotel_825_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2004-08-18", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

825 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_825 <- snotel_825_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_825 <- yearly_wy_aver_825 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_825 <- daily_wy_aver_825 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_825$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_825 <-daily_wy_aver_825 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_825$date_temp <- signif(daily_wy_aver2_825$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_825, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

825 SD

standard_dev_825 <- daily_wy_aver_825 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

standard_dev_all_825 <- standard_dev_825 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_825 <- standard_dev_all_825 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_825 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	4.370755
1989	4.502081
1990	4.094997
1991	4.494781
1992	4.418378
1993	3.862497
1996	4.285971
2000	4.095726
2001	3.960263
2003	3.856046
2004	4.206669
2005	3.688368
2006	4.106063
2007	4.075396
2009	4.002149
2010	4.014554
2011	3.893611
2012	3.781940
2013	4.141614
2014	3.859758
2015	4.069406
2016	3.519394
2017	4.268362
2018	3.604229
2019	3.588746
2020	4.031032
2021	4.007108
2022	4.061986

ggplot(standard_dev_all_825, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 825 average temperatures for water years 2005-2021

MK & SS for 825 (non-corrected)

sd_mk_825 <- mk.test(standard_dev_all_825$sd_2)
print(sd_mk_825)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_825$sd_2
## z = -2.7857, n = 28, p-value = 0.005342
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -142.0000000 2562.0000000   -0.3756614

sd_sens_825 <- sens.slope(standard_dev_all_825$sd_2)
print(sd_sens_825)

## 
##  Sen's slope
## 
## data:  standard_dev_all_825$sd_2
## z = -2.7857, n = 28, p-value = 0.005342
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.033327212 -0.004654193
## sample estimates:
## Sen's slope 
## -0.01801004

Corrected

825 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_825_ad <- snotel_825_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_825_ad <- yearly_wy_aver_825_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_825_ad <- daily_wy_aver_825_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_825_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_825_ad <-daily_wy_aver_825_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_825_ad$date_temp_ad <- signif(daily_wy_aver2_825_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_825_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

825 SS (corrected)

standard_dev_825_ad <- daily_wy_aver_825_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_825_ad <- standard_dev_825_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_825_ad <- standard_dev_all_825_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_825_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	4.093580
1989	4.307244
1990	3.884354
1991	4.315506
1992	4.287504
1993	3.703147
1996	4.092826
2000	3.892889
2001	3.706820
2003	3.609904
2004	4.108226
2005	3.657357
2006	4.106002
2007	4.084842
2009	3.966318
2010	4.017505
2011	3.898041
2012	3.791951
2013	4.165666
2014	3.846573
2015	4.017305
2016	3.520567
2017	4.238999
2018	3.596848
2019	3.602665
2020	4.053922
2021	4.025947
2022	4.072057

ggplot(standard_dev_all_825_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 825 average temperatures for water years 1986-2021

MK & SS 825 (corrected)

sd_mk_825_ad <- mk.test(standard_dev_all_825_ad$sd_2)
print(sd_mk_825_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_825_ad$sd_2
## z = -1.3237, n = 28, p-value = 0.1856
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -68.0000000 2562.0000000   -0.1798942

sd_sens_825_ad <- sens.slope(standard_dev_all_825_ad$sd_2)
print(sd_sens_825_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_825_ad$sd_2
## z = -1.3237, n = 28, p-value = 0.1856
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.020454781  0.005899708
## sample estimates:
##  Sen's slope 
## -0.006032826

Trapper Lake 827 Original 12/13/2004

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_825 <- standard_dev_825 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_825 <- summer_standard_dev_all_825 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_825 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	2.498007
1989	3.350199
1990	3.167237
1991	2.507517
1992	3.212520
1993	3.356008
1996	2.065919
2000	2.640201
2001	3.178698
2003	3.214659
2004	2.905847
2005	3.044575
2006	2.754945
2007	2.620340
2009	2.632170
2010	2.343832
2011	2.493659
2012	2.443842
2013	2.277782
2014	2.558457
2015	2.799886
2016	2.395604
2017	2.140879
2018	2.407780
2019	2.743128
2020	2.943400
2021	3.277573
2022	2.294698

ggplot(summer_standard_dev_all_825, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 825 average summer temperatures for water years 2005-2021

summer MK & SS for 825 (non-corrected)

summer_sd_mk_825 <- mk.test(summer_standard_dev_all_825$sd_2)
print(summer_sd_mk_825)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_825$sd_2
## z = -1.9559, n = 28, p-value = 0.05048
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -100.0000000 2562.0000000   -0.2645503

summer_sd_sens_825 <- sens.slope(summer_standard_dev_all_825$sd_2)
print(summer_sd_sens_825)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_825$sd_2
## z = -1.9559, n = 28, p-value = 0.05048
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.0428372102  0.0004277878
## sample estimates:
## Sen's slope 
## -0.02002212

Winter

winter_standard_dev_all_825 <- standard_dev_825 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_825 <- winter_standard_dev_all_825 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_825 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	4.791046
1989	5.226862
1990	4.564671
1991	5.301219
1992	4.773431
1993	4.172298
1996	4.835181
2000	4.512183
2001	4.158053
2003	4.003286
2004	4.643675
2005	4.193527
2006	4.753575
2007	4.786436
2009	4.728797
2010	4.410692
2011	4.663786
2012	4.378924
2013	4.942928
2014	4.072150
2015	4.739448
2016	4.142515
2017	4.956699
2018	4.079867
2019	3.971509
2020	3.847229
2021	4.196011
2022	4.681897

ggplot(winter_standard_dev_all_825, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 825 average winter temperatures for water years 2005-2021

winter MK & SS for 825 (non-corrected)

winter_sd_mk_825 <- mk.test(winter_standard_dev_all_825$sd_2)
print(winter_sd_mk_825)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_825$sd_2
## z = -2.1139, n = 28, p-value = 0.03452
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## -108.0000000 2562.0000000   -0.2857143

winter_sd_sens_825 <- sens.slope(winter_standard_dev_all_825$sd_2)
print(winter_sd_sens_825)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_825$sd_2
## z = -2.1139, n = 28, p-value = 0.03452
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.041353103 -0.001861425
## sample estimates:
## Sen's slope 
## -0.01890011

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_825_ad <- standard_dev_825_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_825_ad <- summer_standard_dev_all_825_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_825_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	2.264095
1989	3.004068
1990	2.868951
1991	2.271338
1992	2.904141
1993	3.041441
1996	1.864347
2000	2.376586
2001	2.873112
2003	2.833907
2004	2.717289
2005	3.080534
2006	2.730974
2007	2.632687
2009	2.655070
2010	2.346837
2011	2.501445
2012	2.415534
2013	2.255060
2014	2.548523
2015	2.767070
2016	2.364032
2017	2.126034
2018	2.389925
2019	2.761848
2020	2.939172
2021	3.245537
2022	2.299311

ggplot(summer_standard_dev_all_825_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 825 average summer temperatures for water years 1986-2021

summer MK & SS 825 (corrected)

summer_sd_mk_825_ad <- mk.test(summer_standard_dev_all_825_ad$sd_2)
print(summer_sd_mk_825_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_825_ad$sd_2
## z = -0.73099, n = 28, p-value = 0.4648
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -38.0000000 2562.0000000   -0.1005291

summer_sd_sens_825_ad <- sens.slope(summer_standard_dev_all_825_ad$sd_2)
print(summer_sd_sens_825_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_825_ad$sd_2
## z = -0.73099, n = 28, p-value = 0.4648
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02820074  0.01067779
## sample estimates:
##  Sen's slope 
## -0.007702471

Winter

winter_standard_dev_all_825_ad <- standard_dev_825_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_825_ad <- winter_standard_dev_all_825_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_825_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	4.692676
1989	5.140780
1990	4.475759
1991	5.230649
1992	4.706138
1993	4.092225
1996	4.750864
2000	4.350990
2001	4.092541
2003	3.919800
2004	4.540504
2005	4.186796
2006	4.750588
2007	4.789937
2009	4.722557
2010	4.410803
2011	4.661772
2012	4.381019
2013	4.941163
2014	4.073485
2015	4.734769
2016	4.139333
2017	4.966836
2018	4.076670
2019	3.965657
2020	3.847914
2021	4.191345
2022	4.681709

ggplot(winter_standard_dev_all_825_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 825 average winter temperatures for water years 1986-2021

winter MK & SS 825 (corrected)

winter_sd_mk_825_ad <- mk.test(winter_standard_dev_all_825_ad$sd_2)
print(winter_sd_mk_825_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_825_ad$sd_2
## z = -1.5213, n = 28, p-value = 0.1282
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -78.0000000 2562.0000000   -0.2063492

winter_sd_sens_825_ad <- sens.slope(winter_standard_dev_all_825_ad$sd_2)
print(winter_sd_sens_825_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_825_ad$sd_2
## z = -1.5213, n = 28, p-value = 0.1282
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.037595019  0.003057104
## sample estimates:
## Sen's slope 
## -0.01707785

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_825 <- standard_dev_825 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_825 <- spring_standard_dev_all_825 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_825 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	4.761931
1989	4.550399
1990	3.662621
1991	4.554114
1992	3.736155
1993	3.130387
1996	4.234292
2000	4.451921
2001	4.117593
2003	4.580058
2004	4.323378
2005	3.812233
2006	3.625066
2007	4.223224
2009	3.481705
2010	4.137399
2011	3.271553
2012	4.184152
2013	4.343442
2014	4.396963
2015	3.432009
2016	3.420473
2017	4.482418
2018	3.489067
2019	3.667964
2020	4.205916
2021	4.085543
2022	4.354274

ggplot(spring_standard_dev_all_825, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 825 average spring temperatures for water years 2005-2021

spring MK & SS for 825 (non-corrected)

spring_sd_mk_825 <- mk.test(spring_standard_dev_all_825$sd_2)
print(spring_sd_mk_825)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_825$sd_2
## z = -1.0866, n = 28, p-value = 0.2772
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -56.0000000 2562.0000000   -0.1481481

spring_sd_sens_825 <- sens.slope(spring_standard_dev_all_825$sd_2)
print(spring_sd_sens_825)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_825$sd_2
## z = -1.0866, n = 28, p-value = 0.2772
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.03223732  0.01283321
## sample estimates:
## Sen's slope 
## -0.01102705

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_825 <- standard_dev_825 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_825 <- fall_standard_dev_all_825 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_825 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	3.998686
1989	3.180077
1990	4.359677
1991	4.464831
1992	4.827888
1993	4.272250
1996	4.818924
2000	4.460234
2001	3.619401
2003	3.033418
2004	4.170721
2005	2.538015
2006	4.211455
2007	3.496186
2009	3.949427
2010	4.826059
2011	3.438867
2012	3.253248
2013	3.746012
2014	4.311159
2015	3.724828
2016	3.078421
2017	4.215611
2018	3.900683
2019	3.658276
2020	5.338671
2021	4.359969
2022	3.859736

ggplot(fall_standard_dev_all_825, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 825 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 825 (non-corrected)

fall_sd_mk_825 <- mk.test(fall_standard_dev_all_825$sd_2)
print(fall_sd_mk_825)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_825$sd_2
## z = -0.49391, n = 28, p-value = 0.6214
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##             S          varS           tau 
##  -26.00000000 2562.00000000   -0.06878307

fall_sd_sens_825 <- sens.slope(fall_standard_dev_all_825$sd_2)
print(fall_sd_sens_825)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_825$sd_2
## z = -0.49391, n = 28, p-value = 0.6214
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.03835404  0.02867110
## sample estimates:
##  Sen's slope 
## -0.007051284

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_825_ad <- standard_dev_825_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_825_ad <- spring_standard_dev_all_825_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_825_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	4.422774
1989	4.221003
1990	3.443738
1991	4.255919
1992	3.483192
1993	2.864564
1996	3.941142
2000	4.130795
2001	3.826160
2003	4.224862
2004	4.040303
2005	3.815322
2006	3.619536
2007	4.217979
2009	3.494353
2010	4.137487
2011	3.267204
2012	4.158517
2013	4.371532
2014	4.410694
2015	3.393498
2016	3.409133
2017	4.468747
2018	3.516348
2019	3.633739
2020	4.217069
2021	4.083474
2022	4.356690

ggplot(spring_standard_dev_all_825_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 825 average spring temperatures for water years 1986-2021

spring MK & SS 825 (corrected)

spring_sd_mk_825_ad <- mk.test(spring_standard_dev_all_825_ad$sd_2)
print(spring_sd_mk_825_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_825_ad$sd_2
## z = 0.33586, n = 28, p-value = 0.737
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 1.800000e+01 2.562000e+03 4.761905e-02

spring_sd_sens_825_ad <- sens.slope(spring_standard_dev_all_825_ad$sd_2)
print(spring_sd_sens_825_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_825_ad$sd_2
## z = 0.33586, n = 28, p-value = 0.737
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01575352  0.02728554
## sample estimates:
## Sen's slope 
##  0.00311489

Fall

fall_standard_dev_all_825_ad <- standard_dev_825_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_825_ad <- fall_standard_dev_all_825_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_825_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1988	3.715735
1989	3.010989
1990	3.953992
1991	4.154424
1992	4.538382
1993	4.028892
1996	4.486863
2000	4.173198
2001	3.332517
2003	2.808226
2004	4.239526
2005	2.560496
2006	4.163765
2007	3.522553
2009	3.933311
2010	4.866492
2011	3.434236
2012	3.273891
2013	3.766611
2014	4.325807
2015	3.697232
2016	3.037583
2017	4.185972
2018	3.918959
2019	3.691848
2020	5.377291
2021	4.369067
2022	3.895851

ggplot(fall_standard_dev_all_825_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 825 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 825 (corrected)

fall_sd_mk_825_ad <- mk.test(fall_standard_dev_all_825_ad$sd_2)
print(fall_sd_mk_825_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_825_ad$sd_2
## z = 0.41489, n = 28, p-value = 0.6782
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 2.200000e+01 2.562000e+03 5.820106e-02

fall_sd_sens_825_ad <- sens.slope(fall_standard_dev_all_825_ad$sd_2)
print(fall_sd_sens_825_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_825_ad$sd_2
## z = 0.41489, n = 28, p-value = 0.6782
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02268728  0.04212681
## sample estimates:
## Sen's slope 
##  0.00903793

Trapper Lake 827

Original 12/13/2004

snotel_827 <- SNOTEL_yampa_area %>% 
  filter(site_id == "827")

#str(snotel_827) # check the date, usually a character.  

snotel_827$Date <- as.Date(snotel_827$date) #change date from character to date format, capitalize to work with Water year functon from NWIS.

#THIS WILL CHANGE FOR EACH STATION
snotel_827_clean <- snotel_827 %>% # filter for the timeframe
  filter(Date >= "1979-10-01" & Date <= "2022-09-30") %>%
  #filter(temperature_mean >= -30 & temperature_mean <= 20) %>% # removing outliers   
  addWaterYear() %>% 
  mutate(daymonth = format(as.Date(Date), "%d-%m")) %>% 
  na.omit()

#adding water day using difftime (SUPER COOL. example from [this](https://stackoverflow.com/questions/48123049/create-day-index-based-on-water-year))

snotel_827_clean <- snotel_827_clean %>% 
  group_by(waterYear)%>% 
  mutate(waterDay = (as.integer(difftime(Date, ymd(paste0(waterYear - 1 ,'-09-30')), units = "days"))))

# Check for outliers

ggplot(snotel_827_clean, aes(x = Date, y = temperature_mean)) +
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

snotel_827_clean <- snotel_827_clean %>% 
  mutate(temp_diff = abs(temperature_min - temperature_max)) %>% 
  filter(temperature_mean > -40) %>% 
  filter(temperature_mean < 30)

ggplot(snotel_827_clean, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

Per Steven’s advice: :If there are more than 15 missing days, then…remove that year”

# filtering for temperature anomalies
#snotel_827_cull_count <- snotel_827_clean %>% 
#  filter(temperature_min > -40) %>% 
#  count(waterYear)

#snotel_827_cull_count

# filtering for too few observations in a year
snotel_827_cull_count_days <- snotel_827_clean %>% 
  group_by(waterYear) %>% 
  count(waterYear) %>% 
  filter(n < 350)

snotel_827_cull_count_days

## # A tibble: 18 x 2
## # Groups:   waterYear [18]
##    waterYear     n
##        <dbl> <int>
##  1      1986   331
##  2      1994   179
##  3      1995   323
##  4      1996    53
##  5      1997   278
##  6      1999   341
##  7      2001   348
##  8      2002   310
##  9      2003   340
## 10      2004   342
## 11      2009   342
## 12      2010   346
## 13      2011   326
## 14      2013   236
## 15      2014   241
## 16      2016   321
## 17      2017   219
## 18      2019   332

snotel_827_clean_culled <- snotel_827_clean %>% 
  filter(waterYear != "1986" & waterYear != "1994" & waterYear != "1995" & waterYear != "1996" & waterYear != "1997" & waterYear != "1999" & waterYear != "2001" & waterYear != "2002" & waterYear != "2003" & waterYear != "2004" & waterYear != "2009" & waterYear != "2010" & waterYear != "2011" & waterYear != "2013" & waterYear != "2014" & waterYear != "2016" & waterYear != "2017" & waterYear != "2019") #%>% 
  #filter(temperature_mean > -49)

ggplot(snotel_827_clean_culled, aes(x = Date, y = temp_diff)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  #geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature varience (°C)') + 
  xlab('Date')

ggplot(snotel_827_clean_culled, aes(x = Date, y = temperature_mean)) + 
  geom_point() + #lwd = 2) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('Daily temperature (°C)') + 
  xlab('Date')

temp_827_xts <- xts(snotel_827_clean_culled$temperature_mean, order.by = snotel_827_clean_culled$Date)

dygraph(temp_827_xts) %>%
  dyAxis("y", label = "Daily mean temperature (°C)") 

#snotel_827_clean_culled <- snotel_827_clean_culled %>% 
#  filter(temperature_mean > -30)

#temp_827_xts <- xts(snotel_827_clean_culled$temperature_mean, order.by = snotel_827_clean_culled$Date)

#dygraph(temp_827_xts) %>%
#  dyAxis("y", label = "Daily mean temperature (°C)") 

Trapper Lake 827

Original 12/13/2004

snotel_827_adjusted <- snotel_827_clean_culled %>%
  mutate(temp_ad = if_else(Date < "2004-12-13", ((5.3*10^(-7))*(temperature_mean^(4))+(3.72*10^(-5))*(temperature_mean^(3))-(2.16*10^(-3))*(temperature_mean^(2))-(7.32*10^(-2))*(temperature_mean)+1.37)+temperature_mean, temperature_mean))

Non-corrected

827 Detrended

#using the clean culled df:

#average water year temperature

yearly_wy_aver_827 <- snotel_827_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp = mean(temperature_mean))

#Average temperature by day for all water years:

daily_wy_aver_827 <- yearly_wy_aver_827 %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp = mean(temperature_mean))

#average mean temperature by day for the period of record:

daily_wy_aver_827 <- daily_wy_aver_827 %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp = mean(daily_wy_aver_827$aver_day_temp))

# try to show all years as means. 
daily_wy_aver2_827 <-daily_wy_aver_827 %>% 
  group_by(waterDay) %>%
  mutate(date_temp = mean(temperature_mean))
  

daily_wy_aver2_827$date_temp <- signif(daily_wy_aver2_827$date_temp,3) #reduce the sig figs


ggplot(daily_wy_aver2_827, aes(x = waterDay, y = date_temp))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

827 SD

standard_dev_827 <- daily_wy_aver_827 %>% 
  group_by(waterYear) %>% 
  mutate(residual = (all_ave_temp-aver_ann_temp)+temperature_mean-aver_day_temp) %>% 
  mutate(deviation = abs(residual-lag(residual)))

standard_dev_all_827 <- standard_dev_827 %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

standard_dev_all_827 <- standard_dev_all_827 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

standard_dev_all_827 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.827647
1988	4.061811
1989	4.637720
1990	3.836283
1991	3.893497
1992	3.761232
1993	3.877181
1998	3.823371
2000	3.948282
2005	3.538400
2006	4.127193
2007	4.051727
2008	4.006258
2012	3.553023
2015	3.983843
2018	3.654043
2020	4.131457
2021	3.776913
2022	4.102871

ggplot(standard_dev_all_827, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 827 average temperatures for water years 2005-2021

MK & SS for 827 (non-corrected)

sd_mk_827 <- mk.test(standard_dev_all_827$sd_2)
print(sd_mk_827)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_827$sd_2
## z = 0.069971, n = 19, p-value = 0.9442
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##   3.00000000 817.00000000   0.01754386

sd_sens_827 <- sens.slope(standard_dev_all_827$sd_2)
print(sd_sens_827)

## 
##  Sen's slope
## 
## data:  standard_dev_all_827$sd_2
## z = 0.069971, n = 19, p-value = 0.9442
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.02602614  0.01927385
## sample estimates:
## Sen's slope 
## 0.001306779

Corrected

827 Detrended (corrected)

#using the clean culled df:
#average water year temperature
yearly_wy_aver_827_ad <- snotel_827_adjusted %>% 
  group_by(waterYear) %>% 
  mutate(aver_ann_temp_ad = mean(temp_ad))
#Average temperature by day for all water years:
daily_wy_aver_827_ad <- yearly_wy_aver_827_ad %>% 
  group_by(daymonth) %>% 
  mutate(aver_day_temp_ad = mean(temp_ad))
#average mean temperature by day for the period of record:
daily_wy_aver_827_ad <- daily_wy_aver_827_ad %>% 
  group_by(daymonth) %>% 
  mutate(all_ave_temp_ad = mean(daily_wy_aver_827_ad$aver_day_temp_ad))
# try to show all years as means. 
daily_wy_aver2_827_ad <-daily_wy_aver_827_ad %>% 
  group_by(waterDay) %>%
  mutate(date_temp_ad = mean(temp_ad))
  
daily_wy_aver2_827_ad$date_temp_ad <- signif(daily_wy_aver2_827_ad$date_temp_ad,3) #reduce the sig figs
ggplot(daily_wy_aver2_827_ad, aes(x = waterDay, y = date_temp_ad))+
  geom_line(size= 0.7) +
  theme_few() +
  ylab('Average Daily temperature (°C)') + 
  xlab('Day of water year')

827 SS (corrected)

standard_dev_827_ad <- daily_wy_aver_827_ad %>% 
  group_by(waterYear) %>% 
  #filter(waterYear >= 1987 & waterYear <= 2021) %>% 
  mutate(residual = (all_ave_temp_ad-aver_ann_temp_ad)+temp_ad-aver_day_temp_ad) %>% 
  mutate(deviation = abs(residual-lag(residual)))
standard_dev_all_827_ad <- standard_dev_827_ad %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())
standard_dev_all_827_ad <- standard_dev_all_827_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
standard_dev_all_827_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.650798
1988	3.811999
1989	4.436876
1990	3.633448
1991	3.726137
1992	3.595942
1993	3.716321
1998	3.591304
2000	3.741694
2005	3.426567
2006	4.133144
2007	4.070690
2008	4.016840
2012	3.562569
2015	3.915549
2018	3.623543
2020	4.143138
2021	3.788869
2022	4.087724

ggplot(standard_dev_all_827_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 827 average temperatures for water years 1986-2021

MK & SS 827 (corrected)

sd_mk_827_ad <- mk.test(standard_dev_all_827_ad$sd_2)
print(sd_mk_827_ad)

## 
##  Mann-Kendall trend test
## 
## data:  standard_dev_all_827_ad$sd_2
## z = 0.69971, n = 19, p-value = 0.4841
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##          S       varS        tau 
##  21.000000 817.000000   0.122807

sd_sens_827_ad <- sens.slope(standard_dev_all_827_ad$sd_2)
print(sd_sens_827_ad)

## 
##  Sen's slope
## 
## data:  standard_dev_all_827_ad$sd_2
## z = 0.69971, n = 19, p-value = 0.4841
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01687878  0.03400068
## sample estimates:
## Sen's slope 
##  0.01092049

Note: figure captions are incorrect.

Summer and Winter SD NOT-CORRECTED

Summer

summer_standard_dev_all_827 <- standard_dev_827 %>%
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

summer_standard_dev_all_827 <- summer_standard_dev_all_827 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

summer_standard_dev_all_827 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.563520
1988	2.439337
1989	3.071556
1990	2.894219
1991	2.014236
1992	2.822673
1993	2.842504
1998	2.962266
2000	2.568110
2005	2.775151
2006	2.545877
2007	2.215610
2008	2.573560
2012	2.195553
2015	2.387615
2018	2.119442
2020	2.748857
2021	3.007755
2022	2.169263

ggplot(summer_standard_dev_all_827, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 827 average summer temperatures for water years 2005-2021

summer MK & SS for 827 (non-corrected)

summer_sd_mk_827 <- mk.test(summer_standard_dev_all_827$sd_2)
print(summer_sd_mk_827)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_827$sd_2
## z = -1.3295, n = 19, p-value = 0.1837
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##           S        varS         tau 
## -39.0000000 817.0000000  -0.2280702

summer_sd_sens_827 <- sens.slope(summer_standard_dev_all_827$sd_2)
print(summer_sd_sens_827)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_827$sd_2
## z = -1.3295, n = 19, p-value = 0.1837
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.05686104  0.01220211
## sample estimates:
## Sen's slope 
## -0.02237268

Winter

winter_standard_dev_all_827 <- standard_dev_827 %>%
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

winter_standard_dev_all_827 <- winter_standard_dev_all_827 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

winter_standard_dev_all_827 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.700936
1988	4.713817
1989	5.716836
1990	4.449391
1991	4.661980
1992	3.861395
1993	4.626797
1998	4.518215
2000	4.471254
2005	3.997341
2006	5.029591
2007	5.146738
2008	4.723129
2012	4.369610
2015	4.929553
2018	4.389624
2020	4.222537
2021	4.047845
2022	4.922237

ggplot(winter_standard_dev_all_827, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 827 average winter temperatures for water years 2005-2021

winter MK & SS for 827 (non-corrected)

winter_sd_mk_827 <- mk.test(winter_standard_dev_all_827$sd_2)
print(winter_sd_mk_827)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_827$sd_2
## z = -0.83965, n = 19, p-value = 0.4011
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##           S        varS         tau 
## -25.0000000 817.0000000  -0.1461988

winter_sd_sens_827 <- sens.slope(winter_standard_dev_all_827$sd_2)
print(winter_sd_sens_827)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_827$sd_2
## z = -0.83965, n = 19, p-value = 0.4011
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.04768133  0.02675729
## sample estimates:
## Sen's slope 
## -0.02032882

Summer and Winter SD CORRECTED

Summer

summer_standard_dev_all_827_ad <- standard_dev_827_ad %>% 
  filter(waterDay >= 244 & waterDay <= 335) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
summer_standard_dev_all_827_ad <- summer_standard_dev_all_827_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
summer_standard_dev_all_827_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.306756
1988	2.210476
1989	2.739765
1990	2.616480
1991	1.821334
1992	2.541072
1993	2.553339
1998	2.644095
2000	2.331907
2005	2.816581
2006	2.522406
2007	2.242314
2008	2.589671
2012	2.173174
2015	2.362053
2018	2.102200
2020	2.734442
2021	2.967900
2022	2.152661

ggplot(summer_standard_dev_all_827_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 827 average summer temperatures for water years 1986-2021

summer MK & SS 827 (corrected)

summer_sd_mk_827_ad <- mk.test(summer_standard_dev_all_827_ad$sd_2)
print(summer_sd_mk_827_ad)

## 
##  Mann-Kendall trend test
## 
## data:  summer_standard_dev_all_827_ad$sd_2
## z = -0.069971, n = 19, p-value = 0.9442
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -3.00000000 817.00000000  -0.01754386

summer_sd_sens_827_ad <- sens.slope(summer_standard_dev_all_827_ad$sd_2)
print(summer_sd_sens_827_ad)

## 
##  Sen's slope
## 
## data:  summer_standard_dev_all_827_ad$sd_2
## z = -0.069971, n = 19, p-value = 0.9442
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.03338982  0.03447235
## sample estimates:
##  Sen's slope 
## -0.002978772

Winter

winter_standard_dev_all_827_ad <- standard_dev_827_ad %>% 
  filter(waterDay >= 32 & waterDay <= 182) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
winter_standard_dev_all_827_ad <- winter_standard_dev_all_827_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
winter_standard_dev_all_827_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	4.575071
1988	4.587314
1989	5.597093
1990	4.327783
1991	4.577631
1992	3.779147
1993	4.531983
1998	4.396865
2000	4.304574
2005	3.869786
2006	5.034847
2007	5.154815
2008	4.715058
2012	4.376219
2015	4.923204
2018	4.374732
2020	4.214034
2021	4.034780
2022	4.908400

ggplot(winter_standard_dev_all_827_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 827 average winter temperatures for water years 1986-2021

winter MK & SS 827 (corrected)

winter_sd_mk_827_ad <- mk.test(winter_standard_dev_all_827_ad$sd_2)
print(winter_sd_mk_827_ad)

## 
##  Mann-Kendall trend test
## 
## data:  winter_standard_dev_all_827_ad$sd_2
## z = -0.62974, n = 19, p-value = 0.5289
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##           S        varS         tau 
## -19.0000000 817.0000000  -0.1111111

winter_sd_sens_827_ad <- sens.slope(winter_standard_dev_all_827_ad$sd_2)
print(winter_sd_sens_827_ad)

## 
##  Sen's slope
## 
## data:  winter_standard_dev_all_827_ad$sd_2
## z = -0.62974, n = 19, p-value = 0.5289
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.04520030  0.03136811
## sample estimates:
## Sen's slope 
## -0.01131746

Spring and Fall SD NOT-CORRECTED

Spring

spring_standard_dev_all_827 <- standard_dev_827 %>%
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())

spring_standard_dev_all_827 <- spring_standard_dev_all_827 %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

spring_standard_dev_all_827 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.551482
1988	4.270747
1989	4.696154
1990	3.387587
1991	4.185920
1992	3.659416
1993	3.233119
1998	2.992308
2000	4.562073
2005	3.779103
2006	3.446439
2007	3.556846
2008	3.843335
2012	3.700609
2015	3.097907
2018	3.403852
2020	3.784520
2021	3.673243
2022	4.377378

ggplot(spring_standard_dev_all_827, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 827 average spring temperatures for water years 2005-2021

spring MK & SS for 827 (non-corrected)

spring_sd_mk_827 <- mk.test(spring_standard_dev_all_827$sd_2)
print(spring_sd_mk_827)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_827$sd_2
## z = -0.13994, n = 19, p-value = 0.8887
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  -5.00000000 817.00000000  -0.02923977

spring_sd_sens_827 <- sens.slope(spring_standard_dev_all_827$sd_2)
print(spring_sd_sens_827)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_827$sd_2
## z = -0.13994, n = 19, p-value = 0.8887
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.06192107  0.03240055
## sample estimates:
##  Sen's slope 
## -0.009842018

Fall

Fall is split each water year in the middle of the season. This analysis splits the fall season between the preceeding water year and the subsequent water year.

fall_standard_dev_all_827 <- standard_dev_827 %>%
  filter(waterDay >= 336 | waterDay <= 31) %>% 
  group_by(waterYear) %>% 
  mutate(nmbr = n())

fall_standard_dev_all_827 <- fall_standard_dev_all_827 %>% 
  #group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)

fall_standard_dev_all_827 %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.834833
1988	3.308293
1989	3.245410
1990	3.892369
1991	3.670883
1992	3.997704
1993	3.737742
1998	3.713881
2000	3.530093
2005	2.539018
2006	4.071424
2007	3.422620
2008	3.605344
2012	2.791163
2015	2.941302
2018	3.457498
2020	5.441607
2021	3.983392
2022	3.360771

ggplot(fall_standard_dev_all_827, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Non-corrected standard deviation of SNOTEL 827 average fall temperatures for water years 2005-2021. Note that the season is split by the water year.

fall MK & SS for 827 (non-corrected)

fall_sd_mk_827 <- mk.test(fall_standard_dev_all_827$sd_2)
print(fall_sd_mk_827)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_827$sd_2
## z = 0.34986, n = 19, p-value = 0.7264
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  11.00000000 817.00000000   0.06432749

fall_sd_sens_827 <- sens.slope(fall_standard_dev_all_827$sd_2)
print(fall_sd_sens_827)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_827$sd_2
## z = 0.34986, n = 19, p-value = 0.7264
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.03546606  0.08045693
## sample estimates:
## Sen's slope 
##  0.01065753

Spring and Fall SD CORRECTED

Spring

spring_standard_dev_all_827_ad <- standard_dev_827_ad %>% 
  filter(waterDay >= 183 & waterDay <= 243) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
spring_standard_dev_all_827_ad <- spring_standard_dev_all_827_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
spring_standard_dev_all_827_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	3.283306
1988	3.949633
1989	4.352872
1990	3.176078
1991	3.875136
1992	3.390968
1993	2.961022
1998	2.706316
2000	4.195405
2005	3.784639
2006	3.437721
2007	3.540985
2008	3.865635
2012	3.671452
2015	3.047425
2018	3.438750
2020	3.799299
2021	3.655888
2022	4.370353

ggplot(spring_standard_dev_all_827_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 827 average spring temperatures for water years 1986-2021

spring MK & SS 827 (corrected)

spring_sd_mk_827_ad <- mk.test(spring_standard_dev_all_827_ad$sd_2)
print(spring_sd_mk_827_ad)

## 
##  Mann-Kendall trend test
## 
## data:  spring_standard_dev_all_827_ad$sd_2
## z = 0.41983, n = 19, p-value = 0.6746
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
##  13.00000000 817.00000000   0.07602339

spring_sd_sens_827_ad <- sens.slope(spring_standard_dev_all_827_ad$sd_2)
print(spring_sd_sens_827_ad)

## 
##  Sen's slope
## 
## data:  spring_standard_dev_all_827_ad$sd_2
## z = 0.41983, n = 19, p-value = 0.6746
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.03954096  0.05570364
## sample estimates:
## Sen's slope 
##   0.0108003

Fall

fall_standard_dev_all_827_ad <- standard_dev_827_ad %>% 
  filter(waterDay >= 336 | waterDay <= 31) %>%
  group_by(waterYear) %>% 
  mutate(nmbr = n())
fall_standard_dev_all_827_ad <- fall_standard_dev_all_827_ad %>% 
  group_by(waterYear) %>% 
  mutate(resid_mean = mean(residual)) %>%
  mutate(sd_1 = residual-resid_mean) %>% 
  mutate(sd_2 = (((sum((sd_1)^2))/((nmbr-1))))^(0.5)) %>%
  distinct(sd_2, .keep_all = TRUE) %>% 
   select(waterYear, sd_2)
fall_standard_dev_all_827_ad %>% 
  kable(.,'html') %>%
  kable_styling() %>%
  scroll_box(width='250px',height='500px')

waterYear	sd_2
1987	2.659042
1988	3.079897
1989	3.030043
1990	3.562460
1991	3.430062
1992	3.725277
1993	3.504965
1998	3.379884
2000	3.253929
2005	2.246862
2006	4.000100
2007	3.467832
2008	3.555835
2012	2.796832
2015	2.880085
2018	3.483005
2020	5.498296
2021	3.988948
2022	3.408219

ggplot(fall_standard_dev_all_827_ad, aes(x = waterYear, y = sd_2))+
  geom_line(size= 0.7) +
  theme_few() +
  geom_smooth(method = "lm", se=FALSE) +
  ylab('SD') + 
  xlab('Water year')

Morrisey-corrected standard deviation of SNOTEL 827 average fall temperatures for water years 1986-2021. Note that the fall season is split by the water year.

fall MK & SS 827 (corrected)

fall_sd_mk_827_ad <- mk.test(fall_standard_dev_all_827_ad$sd_2)
print(fall_sd_mk_827_ad)

## 
##  Mann-Kendall trend test
## 
## data:  fall_standard_dev_all_827_ad$sd_2
## z = 1.1895, n = 19, p-value = 0.2342
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##           S        varS         tau 
##  35.0000000 817.0000000   0.2046784

fall_sd_sens_827_ad <- sens.slope(fall_standard_dev_all_827_ad$sd_2)
print(fall_sd_sens_827_ad)

## 
##  Sen's slope
## 
## data:  fall_standard_dev_all_827_ad$sd_2
## z = 1.1895, n = 19, p-value = 0.2342
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  -0.01537019  0.08501357
## sample estimates:
## Sen's slope 
##  0.03272511